Question

If f(x) = (e^x)(g(x)), where g(0)=2 and g'(0)=5, find f'(0)

Answer 1

\[\Large f(x)\quad=\quad e^x \;g(x)\]
To find f'(x), we use Product Rule:\[\Large f'(x)\quad=\quad \color{royalblue}{\left(e^x\right)'}g(x)+e^x\color{royalblue}{\left(g(x)\right)'}\]

Answer 2

Taking the derivative of the blue parts gives us:\[\Large f'(x)\quad=\quad e^x\;g(x)+e^x\;g'(x)\]Any confusion so far?