Question

If f(x) = exg(x), where g(0) = 6 and g'(0) = 4, find f '(0).

Answer 1

exg?

Answer 2

\[
f(x) = e^xg(x)
\]This?

Answer 3

Maybe \[
f(x) = e^{xg(x)}
\]

Answer 4

the first one

Answer 5

Okay, then \[
f'(x) = e^xg(x) + e^xg'(x)
\]

Answer 6

\[
f'(0) = e^0g(0)+e^0g'(0)
\]

Answer 7

Can you finish it off?

Answer 8

yes, thank you