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

\[F'(x)=f'(x)g(2x)+2g'(2x)f(x)\] plug in the appropriate numbers to get your answer

Answer 2

i assume the question meant find
\[F'(1)\]

Answer 3

yes it it did... sorry

Answer 4

which rule did u use to set it up btw?

Answer 5

Product rule?

Answer 6

yes i used the product rule, plus the chain rule

Answer 7

because the derivative if
\[g(2x)\] is
\[2\g'(2x)\]

Answer 8

\[2g'(2x)\] i meant

Answer 9

that is how i got
\[F'(x)=f'(x)g(2x)+2g'(2x)f(x)\]

Answer 10

so
\[F'(1)=f'(1)g(2)+2g'(2)f(1)\] then plug in the numbers for the arithmetic

Answer 11

you got this?

Answer 12

im ok for now. thanks!