# Derivative of cosh x

How to find the derivative of the given function by using the derivative of cosh x: formula, 1 example, and its solution.

## Formula

The derivative of cosh x, [cosh x]',

is sinh x.

## Exampley = cosh^{2} x, y' = ?

Solution

Solution (Detail)

y = cosh^{2} x

means

y = (cosh x)^{2}.

This is a composite function of

y = (whole)^{2} and (whole) = cosh x.

So the derivative of the composite function is,

the derivative of the outer function (cosh x)^{2}, 2(cosh x)^{1}

times,

the derivative of the inner function cosh x, sinh x.

2(cosh x)^{1} sinh x = 2 sinh x cosh x

So

2 sinh x cosh x

is the derivative of cosh^{2} x.