# Homework Help: Derivative of f(x) = cos pi*x

1. Nov 7, 2005

### IceColdCola19

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?

2. Nov 7, 2005

### hypermorphism

Are you familiar with the chain rule ?

3. Nov 7, 2005

### James R

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:

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