# Find the derivative of y=sin(pi x)

Trigonometric Functions
Find the derivative of
$$y=\sin(\pi x)$$

The outside function here is $$f(x)=\sin(x)$$. Remember that its derivative is $$\cos(x)$$
The inside function is $$g(x)=\pi x$$. The derivative of this is clearly $$\pi$$.
Putting these together we get $$f′=\cos(\pi x)\times \pi=\pi \cos(\pi x)$$ where the $$\pi x$$ in the coscos function comes from the fact that we also need to remember to put the same argument of the outside function back in when multiplying.