AP Calculus

Question

If F(x) and g(x) are differentiable functions and F(3)=5 F'(3)=-7 g(3)=-1 g'(3)=4, find the derivative of fg at x=3

Answer 1

By the Product Rule, (fg)'(x) = f'(x)g(x)+g'(x)f(x)

 

So, (fg)'(3) = f'(3)g(3)+g'(3)f(3)

 

                = (-7)(-1)+(4)(5) = 27