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

Formula

The derivative of cosh x, [cosh x]',
is sinh x.

Example

Example

Solution

y = cosh2 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 cosh2 x.