If ( f(x)=eˣg(x) ), where ( g(0)=4 ) and ( g'(0)=1 ), find ( f'(0) ). We begin by finding the derivative of ( f(x)=eˣg(x) ). Since this is a product, we use the Product Rule, which states:
a) ( f'(0) = 5e⁰ )
b) ( f'(0) = 4e⁰ )
c) ( f'(0) = e⁰ )
d) ( f'(0) = g(0)e⁰ + g'(0)e⁰ )