Is it true?

Is it true that F(x)=4xe^2x-e^2x+c is an antiderivative of f(x)=4xe^2x
for any constant C?Explain.

Are we supposed to differentiate F(x)?Iam not sure(Thinking)

Quote:

---

Originally Posted by mathcalculushelp

Is it true that F(x)=4xe^2x-e^2x+c is an antiderivative of f(x)=4xe^2x
for any constant C?Explain.

Are we supposed to differentiate F(x)?Iam not sure(Thinking)

---

take the derivative of F(x) ... do you get f(x)?

ok iam differentiating F(x)

here's what i get

i apply product rule for 1st term and second term is as it is..

F(X)=4xe^2x-e^2x+c

(4x)'.(e^2x)-(4x).(e^2x)'-e^2x
(4).e^2x-(4x).e^2x-e^2x
3e^2x-4xe^2x

This is not equal to f(x).Where am I going wrong?