Consider the function f(x)=e^(3x)*g(x) , where g(0)=13 and g′(0)=−2 Find f′(0)

Question

 This is for my homework I need an explanation of how to do this. please

Answer 1

f(x) = e^3xg(x)

 

By the Product Rule, f'(x) = 3e^3xg(x) + e^3xg'(x)

 

So, f'(0) = 3e³⁽⁰⁾g(0) + e³⁽⁰⁾g'(0) = 3(1)(13) + (1)(-2) = 37