Derivative of Hyperbolic Tangent function
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Formula
$\dfrac{d}{dx}{\, \tanh{x}}$ $\,=\,$ $\operatorname{sech^2}{x}$
Introduction
Let $x$ represents a variable, the hyperbolic tangent function is written as $\tanh{x}$ in mathematics. The derivative of the hyperbolic tan function with respect to $x$ is written as follows.
$\dfrac{d}{dx}{\, \tanh{(x)}}$ $\,=\,$ $\operatorname{sech^2}{(x)}$
It is simply written in mathematical form as $(\tanh{x})’$ in differential calculus.
The differentiation of the hyperbolic tan function is equal to the square of hyperbolic secant function.
$\implies$ $\dfrac{d}{dx}{\, \tanh{x}}$ $\,=\,$ $\operatorname{sech^2}{x}$
Other forms
The derivative of hyperbolic tangent can be written in terms of any variable in mathematics.
Example
$(1) \,\,\,$ $\dfrac{d}{dp}{\, \tanh{(p)}}$ $\,=\,$ $\operatorname{sech^2}{(p)}$
$(2) \,\,\,$ $\dfrac{d}{dv}{\, \tanh{(v)}}$ $\,=\,$ $\operatorname{sech^2}{(v)}$
$(3) \,\,\,$ $\dfrac{d}{dy}{\, \tanh{(y)}}$ $\,=\,$ $\operatorname{sech^2}{(y)}$
Proof
Learn how to derive the differentiation of hyperbolic tangent in differential calculus by the first principle of differentiation.
