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

The calculator will find the derivative of $\tanh{\left(x \right)}$, with steps shown.

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

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