The derivative oftanh(x)is: ddxtanh(x)=sech2(x) The Chain Rule: The chain rule is utilized to differentiate composite functions. Ify=f(u), the chain rule applies whenu=g(x), and thereforey=f(g(x)). The derivative ofyis: ...
•tan(x)—tangent •cot(x)—cotangent •arcsin(x)—arcsine •arccos(x)—arccosine •arctan(x)—arctangent •arccot(x)—arccotangent •sinh(x)—hyperbolic sine •cosh(x)—hyperbolic cosine •tanh(x)—hyperbolic tangent ...
Find the derivative and simplify the result. y = tanh^ -1 cos e^ 3x^2 Find the derivative of the following functions: a. f(x) = 3e^2x \sqrt{x} b. f(x) = 4x - 5xe^x c. f(x) = \frac{3x + 1}{x^2 + 4} d. f(x) = \frac{(x + 2)e^x}{(x - 1)} ...
[1/1]Find the first derivative of function tanh(ln(1+ex))x with respect to x: Solution:==Primitive function =xtanh(ln(ex+1))The first derivative function:d(xtanh(ln(ex+1)))dxtanh(ln(ex+1))+xsech2(ln(ex+1))((ex((1)ln(e)+(x)(0)(e)))+0)(ex+1)tanh(ln(ex+1))+...
I am writing some automatic differentiation routines for Taylor series, and would like to verify my results for the value and first six derivatives of ##sinh## and ##cosh## evaluated at ##\pi /3##, and also ##tanh##, and ##sec^2##, evaluated at ##\pi / 4##. I have attempte...
-sin x Tangent tan x Arcsine arcsin x Arccosine arccos x Arctangent arctan x Hyperbolic sine sinh x cosh x Hyperbolic cosine cosh x sinh x Hyperbolic tangent tanh x Inverse hyperbolic sine sinh-1 x Inverse hyperbolic cosine cosh-1 x Inverse hyperbolic tangent tanh-1 xDerivative examplesExamp...
Find the first derivative of the function: y = th(ln\:3x+1 Find the first derivative for function y=x\ln|5x|. Find the first derivative of the function: y = tanh(ln(3x + 1)). Find the first derivative of the function. f(x) = (cos 3x^3)^2 ...
计算公式如下: image.png Python你代码实现: import numpy as np def sigmoid_derivative(x): s = 1 / (1 + np.exp...(x)=tanh′(x)=1−tanh2x=1−(ex−e−xex+e−x)2(5) tanh\_derivative(x) = tanh'(x) = 1 - \tanh^2x = 1- \left...(\frac{e^x-e^{-x}}{e^...
Find the first derivative of the function: \begin{cases} x = \sqrt3{1-\sqrt{t,\\ y = \sqrt{1+\sqrt{t \end{cases}\;\;t \in (1, \infty) Find the first derivative of the function: y = tanh(ln(3x + 1)). Find the first derivative of the function below f(x) = 5x^2 +...
Derivatives: As the given function is trigonometric we must know the derivatives of the trigonometric functions. As the function is the quotient of the two functions we will apply the quotient rule of derivatives: ddxf(x)g(x)=f′(x)g(x)−g′(x)f(x)(g(x))2 ...