Let r(x)= f(g(h(x))), where h(1)=4, g(4)=5, h'(1)=3 , g'(4)=5 and f'(5)=7. find r'(1).

Answer 1

r = f(g(h(x))

r'(x) = f'(g(h(x))) g'(h(x)) h'(x)
r'(1) = f'(g(h(1))) g'(h(1)) h'(1)
= f'(g(4)) g'(4) (3)
= f'(5) (5)(3)
= (7)(5)(3)
= 105