Derivative of $\tanh{\left(x \right)}$

The calculator will find the derivative of

\tanh{\left(x \right)}

, with steps shown.

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Your Input

Find $\frac{d}{dx} \left(\tanh{\left(x \right)}\right)$ .

Solution

The derivative of the hyperbolic tangent is $\frac{d}{dx} \left(\tanh{\left(x \right)}\right) = \operatorname{sech}^{2}{\left(x \right)}$ :

{\color{red}\left(\frac{d}{dx} \left(\tanh{\left(x \right)}\right)\right)} = {\color{red}\left(\operatorname{sech}^{2}{\left(x \right)}\right)}

Thus, $\frac{d}{dx} \left(\tanh{\left(x \right)}\right) = \operatorname{sech}^{2}{\left(x \right)}$ .

Answer

$\frac{d}{dx} \left(\tanh{\left(x \right)}\right) = \operatorname{sech}^{2}{\left(x \right)}$ A