# Derivative of f(x) = cos pi*x

How would I do the derivative of

f(x) = cos pi*x

I know f'(x) cos x = - sin x but what about that pi?

## Answers and Replies

Are you familiar with the chain rule ?

James R
Science Advisor
Homework Helper
Gold Member
The chain rule is

$$\frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx}$$

Take y = cos u

then you know that dy/du = -sin u.

Now put u = nx, for n a constant.

You know that du/dx = n

Now consider:

y = cos nx

Put u = nx, so that y = cos u. Then the chain rule tells us:

$$\frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx}$$
$$= (-\sin u)(n)$$
$$= -n\sin nx$$