# Derivative of cos *x*

How to solve the derivative of cos *x* problems: formula, proof, example, and its solution.

## Formula

The derivative of cos *x* is -sin *x*.

## Proof

cos *x* = sin (*π*/2 - *x*)

Trigonometric functions of (90º - *θ*)

Think sin (*π*/2 - *x*) as a composite function.

Then [sin (*π*/2 - *x*)]' is equal to,

the derivative of the outer part, cos (*π*/2 - *x*)

times, the derivative of the inner part, -1.

Chain rule in differentiation

Derivatives of polynomials

cos (*π*/2 - *x*) = sin *x*

Trigonometric functions of (90º - *θ*)

So [cos *x*]' = -sin *x*.

## Example

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

So *y*' is equal to,

the derivative of the outer part, -sin (*x*^{3} - 4)

times, the derivative of the inner part, 3*x*^{2}.

Chain rule in differentiation

Derivatives of polynomials