Please help I would greatly appreciate it, quiz tomorrow and don't know how to do these.?

Question

question is to find f "(2) of

f(x)= cos(x(pi))^ -2


other problem (same kind):

f(s)= s(1-s^2)^3

I would greatly appreciate it.

Answer 1

Use the chain rule. I'll do the second, and hopefully you can do the first:
f(s) = s*(1-s^2)^3
= g(s)h(s) where g(s) = s and h(s) = (1-s^2)^3
f'(s) = g'(s)h(s) + h'(s)g(s)
= h(s) + s*h'(s)

h'(s) = 3*(1-s^2)^2 * (-2s)
You can combine all the terms to get the answer, and then plug in 2.