How do you find the derivative of ##cos(pi x)##?

The derviative is ##-pisin(pix)##

You must use the chain rule to calculate this derivative since there is a function (##pi*x##) inside of another function (the cosine function ##cos(pix)##).

First, take the derivative of the outside function (which is cosine in this case) without touching the inside and then multiply by the derivative of the inside function (##pix## for this problem).

The derivative of ##cos(x)## is ##-sin(x)## and the derivative of ##pi*x## is ##pi## (since ##pi## is a constant, albeit an irrational one) so the derivative for the entire thing is ##-sin (pi*x) * (pi)##.

Hope that helps!