Derivative of `tanh(x)`

Step-by-step differentiation

Answer

\frac{d}{d x} [tanh (x)]

\frac{1}{c o s h ( x ) ^{2}}

Step-by-step solution

1Derivative of tanh
$\frac{d}{d x} [tanh (x)] = sech^{2} (x)$
The derivative of $tanh (x)$ is $sech^{2} (x)$ .
✓Final Answer
$\frac{d}{d x} [tanh (x)] = \frac{1}{cosh ( x ) ^{2}}$
The first derivative simplifies to $\frac{1}{c o s h ( x ) ^{2}}$ .

Understanding this derivative

Differentiating tanh(x) is a single-rule problem: everything follows from the hyperbolic derivatives. That makes it a good expression for isolating and practicing that one technique.

Hyperbolic functions mirror their trigonometric cousins but without the sign change: sinh differentiates to cosh and cosh to sinh, both positive.

A good way to verify a derivative by hand is to compare it against the step-by-step breakdown above — each step names the rule being applied, so you can pinpoint exactly where your own work diverges if the answers differ.

Learn the rules used here

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Derivative of tanh(x)

Step-by-step solution

Understanding this derivative

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Derivative of `tanh(x)`