Given f(x) = csc^4(5x^2-3x+1), find f'(x). Show all work.

Answer 1

If u = 5x^2-3x+1,

f(u) = csc^4(u)
f'(x) = f'(u)*u' = 4 csc^3(u) (-csc(u)cot(u)) u'
u' = 10x-3

Now just do the substitution.