Let f(x)=(x^2)(e^5x)

find the derivative f'(x) and the second derivative, f"(x)

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!

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