# Derivative of cos x

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

## Formula

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

is -sin x.

## Exampley = cos (x^{3} - 4), y' = ?

Solution

Solution (Detail)

y = cos (x^{3} - 4)

is a composite function of

y = cos (whole) and (whole) = x^{3} - 4.

So the derivative of the composite function is,

the derivative of the outer function cos (x^{3} - 4), -sin (x^{3} - 4)

times,

the derivative of the inner function x^{3} - 4, 3x^{2}.

Arrange the expression.

So

-3x^{2} sin (x^{3} - 4)

is the derivative of cos (x^{3} - 4).