Question

Suppose F(x)=f(x)g(2x) . If f(1)=3 , f′(1)=1 , g(2)=2 , and g′(2)=5 , find F′(1) .

Answer 1

oh no

Answer 2

need both the product and the chain rule, which is the whole point of this problem

Answer 3

\[F(x)=f(x)g(2x)\]
\[F'(x)=f'(x)g(2x)+f(x)g'(2x)\times 2\]