<span>Use the product rule!
f(x) = (x^2)(e^5x)
First times the derivative of the second, plus, second times the derivative of the first:
(d/dx) f(x) = (x^2) d/dx(e^5x) + (e^5x) d/dx (x^2)
what's the derivative of e^5x? well you have to chain rule for that:
d/dx (e^5x) = (e^5x) (5)
now what is the derivative of x^2? yup! just 2
d/dx (x^2) = 2
so what's f'(x)? Let's just plug in our derivatives
f'(x) = (x^2) (e^5x) (5) + (e^5x)(2)
tada!</span>