So in this case, the derivative of f(x) = cos pi*x is f'(x) = -pi*sin pi*x.

[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?

 

[hypermorphism]

Are you familiar with the chain rule ?

 

[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:

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