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# Tanh function

The hyperbolic tangent function is an old mathematical function. It was first used in the work by L'Abbe Sauri (1774). It was first used in the work by L'Abbe Sauri (1774). This function is easily defined as the ratio between the hyperbolic sine and the cosine functions (or expanded, as the ratio of the half‐difference and half‐sum of two exponential functions in the points and ) Die Funktion Tanh berechnet hier den hyperbolischen Tangens reeller Zahlen. Die Tanh Funktion zur Berechnung einer komplexen Zahl finden Sie hier. Eingabe Der Winkel wird in Grad (Vollkreis = 360°) oder Radiant (Vollkreis = 2 · π) angegeben. Die verwendete Maßeinheit wird mit dem Menü Grad oder Radiant eingestellt Die obige Tabelle zeigt, dass es rechnerisch keinen Unterschied macht, ob die Argumente ($$x$$-Werte) der Funktion im Gradmaß oder im Bogenmaß vorliegen. Zur Darstellung von trigonometrischen Funktionen in einem Koordinatensystem ist es allerdings üblich, das Bogenmaß zu verwenden. Zur Erinnerung: $$360°$$ (Gradmaß) entsprechen $$2\pi$$ (Bogenmaß). Die Abbildung zeigt den Graphen der.

The pure tanh () function shows this behaviour, it returns values close to -1 for x<<0 and values close to 1 for x>>0. We define our new function s (x) = 0.5+0.5 tanh ((x-a)/b). The function was shifted to return values between 0 and 1 and the parameters a and b can be used to define the switch point and the smoothing level Tanh. class torch.nn.Tanh [source] Applies the element-wise function: Tanh ( x) = tanh ⁡ ( x) = exp ⁡ ( x) − exp ⁡ ( − x) exp ⁡ ( x) + exp ⁡ ( − x) \text {Tanh} (x) = \tanh (x) = \frac {\exp (x) - \exp (-x)} {\exp (x) + \exp (-x)} Tanh(x) = tanh(x) = exp(x)+exp(−x)exp(x)−exp(−x) The tanh function, a.k.a. hyperbolic tangent function, is a rescaling of the logistic sigmoid, such that its outputs range from -1 to 1. (There's horizontal stretching as well.) $tanh(x) = 2 g(2x) - 1$ It's easy to show the above leads to the standard definition $$tanh(x) = \frac{e^x - e^{-x}}{e^x + e^{-x}}$$. The (-1,+1) output range tends to be more convenient for neural networks, so tanh functions show up there a lot 2. Tanh or Hyperbolic tangent: Tanh help to solve non zero centered problem of sigmoid function. Tanh squashes a real-valued number to the range [-1, 1]. It's non-linear too corresponding to the derived trigonometric functions. The inverse hyperbolic functions are: area hyperbolic sine arsinh (also denoted sinh −1 , asinh or sometimes arcsinh) area hyperbolic cosine arcosh (also denoted cosh −1 , acosh or sometimes arccosh. and so on

### Introduction to the Hyperbolic Tangent Function

• tanh x x x x e e x x x sinh cosh coth Daraus ergibt sich: tanhx 1 und cothx ! 1. tanhx ist dabei über den gesamten Definitionsbereich stetig. cothx ist unstetig bei x 0 . Beide Funktionen haben einen Grenzwert von 1 für xo f und von -1 für xo f. Desweiteren gilt: x x x 1 tanh2 2tanh tanh2 y; x y x y x 1 tanh tanh tanh( ) r r r Weiterhin lassen sich die Funktionen - Secans Hyperbolicus x hx.
• The notation thz is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). tanhz is implemented in the Wolfram Language as Tanh[z]. Special values include tanh0 = 0 (5) tanh(lnphi) = 1/5sqrt(5), (6) where phi is the..
• Die reelle Funktion ist streng monoton steigend und besitzt in = ihren einzigen Wendepunkt. Die reelle Funktion cosh {\displaystyle \cosh } ist für auf dem Intervall ( − ∞ , 0 ] {\displaystyle (-\infty ,0]} streng monoton fallend, auf dem Intervall [ 0 , ∞ ) {\displaystyle [0,\infty )} streng monoton steigend und besitzt bei x = 0 {\displaystyle x=0} ein globales Minimum
• Weil tanh () eine statische Funktion von Math ist, wird es immer als Math.tanh () eingesetzt, jedoch nicht als Methode eines erzeugten Math Objektes (Math ist kein Konstruktor)
• Hyperbolic Tangent Function (aka tanh) The function produces outputs in scale of [-1, +1]. Moreover, it is continuous function. In other words, function produces output for every x value. Derivative of Hyperbolic Tangent Function. Before we begin, let's recall the quotient rule. Suppose that function h is quotient of fuction f and function g. If derivatives exist for both function f and.
• The inverse hyperbolic tangent (Zwillinger 1995, p. 481; Beyer 1987, p. 181), sometimes called the area hyperbolic tangent (Harris and Stocker 1998, p. 267), is the multivalued function that is the inverse function of the hyperbolic tangent. The function is sometimes denoted (Jeffrey 2000, p. 124) or (Gradshteyn and Ryzhik 2000, p. xxx)
• Public Shared Function Tanh (value As Double) As Double Parameters. value Double. An angle, measured in radians. Returns Double. The hyperbolic tangent of value. If value is equal to NegativeInfinity, this method returns -1. If value is equal to PositiveInfinity, this method returns 1. If value is equal to NaN, this method returns NaN. Examples. The following example uses Tanh to evaluate.

### Tanh - hyperbolischen Tangens online berechne

1. Wichtige Informationen zur TANH-Funktion in Excel. Machen Sie sich zunächst mit den Grundlagen einer Hyperbel und anderen Trigonometriekonzepten vertraut. Ohne diese Funktionen zu verstehen, ist es sehr schwierig, Trigonometriefunktionen in Excel zu verstehen. Sie sollten in diesen Konzepten stark sein. Versuchen Sie, die Probleme manuell zu lösen und lernen Sie diese Funktion in Excel.
2. Tanh is the hyperbolic tangent function, which is the hyperbolic analogue of the Tan circular function used throughout trigonometry. Tanh [α] is defined as the ratio of the corresponding hyperbolic sine and hyperbolic cosine functions via . Tanh may also be defined as , where is the base of the natural logarithm Log. Tanh automatically evaluates to exact values when its argumen
3. The range of the tanh function is from (-1 to 1). tanh is also sigmoidal (s - shaped). Fig: tanh v/s Logistic Sigmoid The advantage is that the negative inputs will be mapped strongly negative and the zero inputs will be mapped near zero in the tanh graph. The function is differentiable

### Tangensfunktion - Mathebibel

Hyperbolic tangent function. TANH (x) returns the hyperbolic tangent of the angle x. The argument x must be expressed in radians. To convert degrees to radians you use the RADIANS function / Activation function Calculates the tanh(x) (Tangent Hyperbolic Function). tanh(x) function is used in the activation function of the neural network

### Smooth transition between functions with tanh() - Jörg Rädle

Y = tanh (X) returns the hyperbolic tangent of the elements of X. The tanh function operates element-wise on arrays. The function accepts both real and complex inputs. All angles are in radians Im Allgemeinen ist eine Sigmoidfunktion eine beschränkte und differenzierbare reelle Funktion mit einer durchweg positiven oder durchweg negativen ersten Ableitung und genau einem Wendepunkt.. Außer der logistischen Funktion enthält die Menge der Sigmoidfunktionen den Arkustangens, den Tangens hyperbolicus und die Fehlerfunktion, die sämtlich transzendent sind, aber auch einfache. tanh and sigmoid, both are monotonically increasing function that asymptotes at some finite value as +inf and-inf is approached. Infact, tanh is a wide variety of sigmoid functions including. Python tanh() Python tanh() is an inbuilt method that is defined under the math module, which is used to find the hyperbolic tangent of the given parameter in radians. For instance, if x is passed as an argument in tanh function (tanh(x)), it returns the hyperbolic tangent value. Syntax math.tanh(var The function that essentially needs to be executed to arrive at ReLU is a max function: $$max(0, x)$$ produces 0 when $$x < 0$$ and x when $$x >= 0$$. That's ReLU! Now compare this with the formulas of the Sigmoid and tanh functions presented above: those contain exponents. Computing the output of a max function is much simpler and less.

The range of the tanh function is [-1,1] and that of the sigmoid function is [0,1] Avoiding bias in the gradients. This is explained very well in the paper, and it is worth reading it to understand these issues. share | cite | improve this answer | follow | edited Mar 28 '18 at 11:36. Peter Flom . 91k 17 17 gold badges 135 135 silver badges 263 263 bronze badges. answered Jun 8 '14 at 6:47. The atanh function acts on X element-wise. X = [2 -3 1+2i]; Y = atanh (X) Y = 1×3 complex 0.5493 + 1.5708i -0.3466 - 1.5708i 0.1733 + 1.1781i Plot the Inverse Hyperbolic Tangent Function

The basic hyperbolic functions, cosh, sinh and tanh are related to the equilateral hyperbola, x 2-y 2 =1.. If the area between a line through the origin, the x-axis, and the hyperbola x 2-y 2 =1 has area α/2, then:. cosh α is the x coordinate of the intersection between the line through the origin and the hyperbola x 2-y 2 =1; sinh α is the y coordinate of the intersection between the line. It lags behind the Sigmoid and Tanh for some of the use cases. Further reading. Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification, Kaiming He et al . (2015) Sigmoid ¶ Sigmoid takes a real value as input and outputs another value between 0 and 1. It's easy to work with and has all the nice properties of activation functions: it's non-linear. Die TANH-Funktion verwendet Radiant, es sei denn, Sie geben eine andere Maßeinheit im Winkel an. The TANH function uses radians unless you specify a different unit of measure in angle. Beispiel Example. TANH (-45) TANH(-45) Gibt -0,6558 zurück. Returns -0.6558. Ähnliche Artike TanH function in excel is a mathematical trigonometry function that is used for calculating Hyperbolic tangent of any number. We can use the TanH function directly just by selecting any number which we want to convert into a hyperbolic tangent figure irrespective of any type of number we use in This function returns hyperbolic tangent of x. Example. The following example shows the usage of tanh() function. #include <stdio.h> #include <math.h> int main { double x, ret; x = 0.5; ret = tanh(x); printf(The hyperbolic tangent of %lf is %lf degrees, x, ret); return(0); } Let us compile and run the above program that will produce the following result �

### Tanh — PyTorch 1.7.0 documentatio

Die Tanh-Funktion wird hauptsächlich zur Klassifizierung zwischen zwei Klassen verwendet. 3. ReLU (Rectified Linear Unit) Aktivierungsfunktion. Die ReLU ist derzeit die am häufigsten verwendete Aktivierungsfunktion der Welt. Seit neustem wird sie in fast allen konvolutionellen neuronalen Netzwerken bzw. im Deep Learning eingesetzt. ReLU Aktivierungsfunktion. Wie man sieht, ist die ReLU (von. Y = tanh(X) returns the hyperbolic tangent of the elements of X. The tanh function operates element-wise on arrays. The function accepts both real and complex inputs. All angles are in radians tanh(x) function result T a n g e n t h y p e r b o l i c f u n c t i o n tanh ( x ) f ( x ) = tanh ( x ) = e x − e − x e x + e − x f ′ ( x ) = 1 − f ( x ) 2 f ′′ ( x ) = − 2 f ( x ) { 1 − f ( x ) 2 } T a n g e n t h y p e r b o l i c f u n c t i o n tanh ⁡ ( x ) f ( x ) = tanh ⁡ ( x ) = e x − e − x e x + e − x f ′ ( x ) = 1 − f ( x ) 2 f ″ ( x ) = − 2 f ( x ) { 1 − f ( x ) 2 numpy.tanh¶ numpy.tanh (x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True [, signature, extobj]) = <ufunc 'tanh'>¶ Compute.

Kurvendiskussion: f(x) = tanh(x) Funktion . f(x) = tanh(x) = (e^x - e^{-x}) / (e^x + e^{-x}) = (e^{2·x} - 1)/(e^{2·x} + 1) (i) maximalen Deﬁnitionsbereich finden. D = R . Der Nenner darf nur nicht 0 werden. Da die e-Funktion aber immer > 0 ist, kann der Nenner hier nie null werden. (ii) Symmetrieeigenschaften der Funktion untersuchen It is also known as the hyperbolic tangent activation function. Similar to sigmoid, tanh also takes a real-valued number but squashes it into a range between -1 and 1. Unlike sigmoid, tanh outputs are zero-centered since the scope is between -1 and 1. You can think of a tanh function as two sigmoids put together

The tanh function is just another possible functions that can be used as a nonlinear activation function between layers of a neural network. It actually shares a few things in common with the sigmoid activation function. They both look very similar. But while a sigmoid function will map input values to be between 0 and 1, Tanh will map values to be between -1 and 1 Tanh function, the formula is: Basically, it is. sinh (x) / cosh (x) the x value we input will mapping between [-1, 1]. And I wrote a simple code to display: # -*- coding: utf-8 -*- import matplotlib.pyplot as plt import math value = -10 x = [value + n *0.01 for n in range ( 2001 )] y = [math. tanh (v) for v in x] plt. plot (x, y) ax = plt. gca. Hyperbolic Functions. The two basic hyperbolic functions are sinh and cosh: Hyperbolic Sine: sinh(x) = e x − e −x 2 (pronounced shine) Hyperbolic Cosine: cosh(x) = e x + e −x 2 (pronounced cosh) They use the natural exponential function e x. And are not the same as sin(x) and cos(x), but a little bit similar: sinh vs sin. cosh vs cos. Catenary. One of the interesting uses of. inverse tanh(x)an expression for tanh^-1(x)see playlist for more: https://www.youtube.com/playlist?list=PLj7p5OoL6vGzuzhYkqsR4_O3GIKe5-_29&disable_polymer=tru

Illustrated definition of Tanh: The Hyperbolic Tangent Function. tanh(x) sinh(x) cosh(x) (esupxsup minus esupminusxsup).. Die Tanh-Funktion hingegen hat eine Ableitung von bis zu 1,0, wodurch die Aktualisierungen von W und b viel größer werden. Dies macht die tanh-Funktion fast immer besser als Aktivierungsfunktion (für versteckte Schichten) als die Sigmoid-Funktion

The syntax for the TANH function in Oracle/PLSQL is: TANH( n ) Parameters or Arguments n A numberic value used to calculate the hyperbolic tangent tanh (float $arg) : float Returns the hyperbolic tangent of arg, defined as sinh (arg)/cosh (arg) ### Activation Functions: Sigmoid, Tanh, ReLU, Leaky ReLU 1. Thus, like the α-tanh spiral, the log-tanh spiral rotation function also has 6 free parameters: θ out, r in, r out, r ws, θ incl, θ sky PA. Note that in terms of ca-pabilities, the α-tanh function can often reproduce the log-tanh function and more. Therefore, the α-tanh is probably a more useful rotation function in practice 2. g language. Syntax of tanh () Function 3. In diesem Artikel werden die Formelsyntax und die Verwendung der Funktion TANHYP in Microsoft Excel beschrieben. Beschreibung. Gibt den hyperbolischen Tangens einer Zahl zurück. Syntax. TANHYP(Zahl) Die Syntax der Funktion TANHYP weist die folgenden Argumente auf: Zahl Erforderlich. Eine beliebige reelle Zahl. Hinwei 4. def tanh_function(x): z = (2/(1 + np.exp(-2*x))) -1 return z tanh_function(0.5), tanh_function(-1) Output: (0.4621171572600098, -0.7615941559557646) As you can see, the range of values is between -1 to 1. Apart from that, all other properties of tanh function are the same as that of the sigmoid function. Similar to sigmoid, the tanh function is continuous and differentiable at all points. Let. 5. See TANH Function. Hyperbolic Cotangent. Computed as 1/TANH. Hyperbolic Secant. Computed as 1/COSH. Hyperbolic Cosecant. Computed as 1/SINH. Source: In the following sample, input values are in degrees: X-30: 0: 30: 45: 60: 90: 120: 135: 180: Transformation: In this example, all values are rounded to three decimals for clarity. First, the above values in degrees must be converted to radians. self.tanh = nn.Tanh() Whereas I can use nn.functional.tanh directly in my_model.forward(), e.g. output = nn.functional.tanh(input) If you deprecate nn.functional.tanh I could do. output = nn.Tanh()(input) where ever I need the functional form, but it would be slower because of the class instantiation. What has this to do with Variables and. The tanh function on the other hand, has a derivativ of up to 1.0, making the updates of W and b much larger. This makes the tanh function almost always better as an activation function (for hidden layers) rather than the sigmoid function. To prove this myself (at least in a simple case), I coded a simple neural network and used sigmoid, tanh and relu as activation functions, then I plotted. Berechnen Sie die Umkehrfunktion der Funktion tanh explizit. Setzen Sie dazu die Definition von tanh in die Gleichung $$x=\tanh y$$ ein und lösen Sie diese nach $$y$$ auf. Untersuchen Sie weiters den Definitionsbereich dieser Umkehrfunktion, welche mit artanh bezeichnet wird. Hinweis: Seite 129 im Skriptum zur Vorlesung. Ich bin für jede Hilfe dankbar :) besagte Seite 129 möchte ich. The math.tanh() function returns the hyperbolic tangent value of a number. Syntax: math.tanh(x) Parameter:This method accepts only single parameters. x :This parameter is the value to be passed to tanh() Returns:This function returns the hyperbolic tangent value of a number. Below examples illustrate the use of above function: Example 1: filter_none. edit close. play_arrow. link brightness_4. Similar Functions. Other C functions that are similar to the tanh function: cosh function <math.h> sinh function <math.h> See Also. Other C functions that are noteworthy when dealing with the tanh function: acos function <math.h> asin function <math.h> atan function <math.h> atan2 function <math.h> cos function <math.h> sin function <math.h> TANH returns the hyperbolic tangent of n. This function takes as an argument any numeric data type or any nonnumeric data type that can be implicitly converted to a numeric data type. If the argument is BINARY_FLOAT, then the function returns BINARY_DOUBLE. Otherwise the function returns the same numeric data type as the argument. See Also: Table 2-8 for more information on implicit conversion. Inverse functions . If y = sinh(x), we can define the inverse function x = sinh-1 y, and similarly for cosh and tanh. The inverses of sinh and tanh are uniquely defined for all x. For cosh, the inverse does not exist for values of y less than 1. For y = 1, x = 0. For y > 1, there will be two corresponding values of x, of equal absolute value. Hyperbolic Tangent Function for Numeric and Symbolic Arguments. Depending on its arguments, tanh returns floating-point or exact symbolic results. Compute the hyperbolic tangent function for these numbers The role of activation functions in a Neural Network Model; Three types of activation functions -- binary step, linear and non-linear, and the importance of non-linear functions in complex deep learning models; Seven common nonlinear activation functions and how to choose an activation function for your model—sigmoid, TanH, ReLU and mor Definition and Usage. The tanh() function returns the hyperbolic tangent of a number, which is equal to sinh(x)/cosh(x) ### Hyperbolic functions - Wikipedi torch.nn.functional.embedding (input, weight, padding_idx=None, max_norm=None, norm_type=2.0, scale_grad_by_freq=False, sparse=False) [source] ¶ A simple lookup table that looks up embeddings in a fixed dictionary and size. This module is often used to retrieve word embeddings using indices. The input to the module is a list of indices, and. Tanh ist eine gute Funktion mit der oben genannten Eigenschaft. Eine gute Neuroneneinheit sollte begrenzt, leicht differenzierbar, monoton (gut für konvexe Optimierung) und einfach zu handhaben sein. Wenn Sie diese Qualitäten betrachten, dann glaube ich,. Viele übersetzte Beispielsätze mit tanh function - Deutsch-Englisch Wörterbuch und Suchmaschine für Millionen von Deutsch-Übersetzungen tanh(data_type x) Parameter :The function accepts one mandatory parameter x which specifies the hyperbolic angle in radian. The parameter can be of double, float or long double datatype. Return Value:The function returns the hyperbolic tangent of the argument. Below programs illustrate the above method TANH Function in Excel. In trigonometry we have a term called hyperbolic tangent which is the ratio of the hyperbolic sine and cosine functions, to calculate this mathematical operation in excel we have an inbuilt trigonometric function known as TANH and it takes single argument as an input. TANH function is categorized as Math, or Trig function in excel returns the hyperbolic tangent function. Computes hyperbolic tangent of x element-wise 1. Hyperbolic Functions Description. These functions give the obvious hyperbolic functions. They respectively compute the hyperbolic cosine, sine, tangent, and their inverses, arc-cosine, arc-sine, arc-tangent (or 'area cosine', etc). Usage cosh(x) sinh(x) tanh(x) acosh(x) asinh(x) atanh(x) Arguments. x: a numeric or complex vector. Details. These are internal generic primitive functions. 2. The hyperbolic tangent (tanh) and logistic sigmoid ($\sigma\$) functions are defined as follows: And if we'd plot those functions side-by-side, the relationship can almost be picked out by eye: Since the logistic sigmoid function is symmetric around the origin and returns a value in range [0, 1], we can write the following relationship: I.e.
3. g round the.
4. The tanh() function takes a single argument in radians and returns the hyperbolic tangent of that angle in type double, float or long double type. The hyperbolic tangent of x is given by, tanh() Parameters. The tanh() function takes a single mandatory argument representing a hyperbolic angle in radian. tanh() Return value . The tanh() function returns the hyperbolic tangent of the argument.
5. Um diese Funktion zu verwenden, wählen Sie Berechnen > Rechner aus.. Berechnet den Tangens Hyperbolicus eines Winkels. Die hyperbolischen Trigonometriefunktionen basieren auf der Hyperbel mit der Gleichung x 2 - y 2 = 1. Diese Funktionen weichen von denen in der Standardtrigonometrie (zirkulär) ab, deren Funktionen auf dem Einheitskreis mit der Gleichung x 2 + y 2 = 1 beruhen

11. 12. /* tanh example */#include <stdio.h> /* printf */#include <math.h> /* tanh, log */intmain (){ doubleparam, result; param = log(2.0); result = tanh (param); printf (The hyperbolic tangent of %f is %f.\n, param, result); return0;} Output The TANH function returns the hyperbolic tangent of the argument, where the argument is an angle, expressed in radians. >>-TANH (numeric-expression)------------------------------------>< The schema is SYSIBM. The TANH and ATANH functions are inverse operations tanh(x) Extended Keyboard; Upload; Examples; Random; Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people. The tanh function returns the hyperbolic tangent of x. Products Download Events Support Videos All Product Families ARM7, ARM9, and Cortex-M3 Products C16x, XC16x, and ST10 Products C251 and 80C251 Products Cx51 and 8051 Product computes hyperbolic tangent of a complex number (tanh(z)) (function template) tanh (std::valarray) applies the function std::tanh to each element of valarray (function template) C documentation for tanh. Retrieved from https.     tanh 4x = (4 tanh x + 4 tanh 3 x)/(1 + 6 tanh 2 x + tanh 4 x) POWERS OF HYPERBOLIC FUNCTIONS. sinh 2 x = ½cosh 2x — ½. cosh 2 x = ½cosh 2x + ½. sinh 3 x = ¼sinh 3x — ¾sinh x. cosh 3 x = ¼cosh 3x + ¾cosh x. sinh 4 x = 3/8 - ½cosh 2x + 1/8cosh 4x. cosh 4 x = 3/8 + ½cosh 2x + 1/8cosh 4x. SUM, DIFFERENCE AND PRODUCT OF HYPERBOLIC. Tanh is a good function with the above property. A good neuron unit should be bounded, easily differentiable, monotonic (good for convex optimization) and easy to handle. If you consider these qualities, then i believe you can use ReLU in place of tanh function since they are very good alternatives of each other Hyperbolic Functions Properties. The point (cos (t), sin (t)) is on the unit circle x 2 + y 2 = 1. The point (cosh (t), sinh (t)) is on the hyperbola x 2 - y 2 = 1. Graphs of hyperbolic functions: f (x) = sinh (x), f (x) = csch (x), f (x) = cosh (x), f (x) = sech (x), f (x) = tanh (x), f (x) = coth (x) The derivative is: 1-tanh^2(x) Hyperbolic functions work in the same way as the normal trigonometric cousins but instead of referring to a unit circle (for sin, cos and tan) they refer to a set of hyperbolae. (Picture source: Physicsforums.com) You can write: tanh(x)=(e^x-e^(-x))/(e^x+e^-x) It is now possible to derive using the rule of the quotient and the fact that: derivative of e^x is e^x and derivative of e^-x is -e^-x So you have: d/dxtanh(x)=[(e^x+e^-x)(e^x+e^-x)-(e^x-e. The basic hyperbolic functions are: hyperbolic sine sinh (/ ˈ s ɪ ŋ, ˈ s ɪ n tʃ, ˈ ʃ aɪ n /), hyperbolic cosine cosh (/ ˈ k ɒ ʃ, ˈ k oʊ ʃ /), from which are derived: hyperbolic tangent tanh (/ ˈ t æ ŋ, ˈ t æ n tʃ, ˈ θ æ n /), hyperbolic cosecant csch or cosech (/ ˈ k oʊ s ɛ tʃ, ˈ k oʊ ʃ ɛ k /) hyperbolic secant sech (/ ˈ s ɛ tʃ, ˈ ʃ ɛ k /) I want to show a function which includes the tanh of a fraction, i.e. \tanh(\frac{x - g}{h}) but which gives me the normal small parentheses. I already tried \tanh$$\frac{x - g}{h}$$ but this just omits the parentheses at all. So how can I get large parentheses which enclose the entire fraction

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