What is the derivative of x*e^(2x)?

I know that I have to use integration by parts. However, I am not sure if I got the right answer.

Thank you!

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- Feb 23rd 2013, 04:17 AMremutyteWhat is the derivative of xe^(2x)?
What is the derivative of x*e^(2x)?

I know that I have to use integration by parts. However, I am not sure if I got the right answer.

Thank you! - Feb 23rd 2013, 05:07 AMMINOANMANRe: What is the derivative of xe^(2x)?
The first derivative is e^(2x)[1+2x] and the second is 4e^(2x)[x+1]

- Feb 26th 2013, 01:06 AMjohnykeetsRe: What is the derivative of xe^(2x)?
As far as my knowledge is concerned, The derivative can be calculated by

using d/dx(uv) = u dv/dx + v du/dx

d/dx(xe^2x) = x d/dx(e^2x) + e^2x as d/dx x = 1

= 2x e^2x + e^2x as d/dx(e^y) = e^y dy/dx [using chain rule]

Therefore, the derivative of xe^(2x)=1.

Hope this is useful.

maths homework

maths assignments help - Feb 26th 2013, 03:16 AMHallsofIvyRe: What is the derivative of xe^(2x)?
What, exactly is the

**question**? You first ask about the derivative but then refer to integration.

If the question is about the derivative, you use the product rule: $\displaystyle (xe^x)'= (x)'e^x+ x(e^x)'= e^x+ xe^x= (x+ 1)e^x$.

If the question is about the integral, you use integration by parts. Let u= x, $\displaystyle dv= e^xdx$. Then du= dx, $\displaystyle v= e^x$.

$\displaystyle \int xe^x dx= xe^x- \int e^x dx= xe^x- e^x+ C= (x- 1)e^x+ C$.