Question

If F(x)=f(g(x)-h(x)), where g(3)=5, h(3)=4, g'(3)=3, h'(3)=1 and f'(1)=10, find F'(3).

I know how to do derivatives and all, but I rlly can't figure this question out

Answer 1

recall the chain rule if

F = f(u)
and u is a function of x, then

dF/dx = df/du du/dx
F'(3) = f'(g(3)-h(3))(g'(3)-h'(3))
= f'(5-4)(3-1)
= f'(1)(2)
= 10*2
= 20