if f(x)=e^xg(x), where g(0)=1 and g’(0)=4, find f’(0)

Answer 1

f(x) = e^x.g(x) you need to know

derivative e^u(x) = u'(x) e^u(x)

Example:

derivative e^(2x) = 2 e^(2x)

f'(x) = ( g(x) + X.g'(x)) * e^xg(x) (derivative of exponent follows product rule)

f'(0) = (g(0) + 0 g'(0)) * e^0g(0)

f'(x) = ( 1 + 0 ) * e^0

f'(x) = 1 * 1 = 1

I hope it is useful,

Minoo