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

Formula

The derivative of cos x, [cos x]',
is -sin x.

Example

Example

Solution

y = cos (x3 - 4) is a composite function of
y = cos (whole) and (whole) = x3 - 4.

So the derivative of the composite function is,
the derivative of the outer function cos (x3 - 4), -sin (x3 - 4)
times,
the derivative of the inner function x3 - 4, 3x2.

Arrange the expression.

So -3x2 sin (x3 - 4) is the derivative of cos (x3 - 4).