## TechnoFiction 2 years ago Can anyone help me with the derivative of: y=x^11 e^x

1. TechnoFiction

$y=x ^{11}e ^{x}$ Much easier to look at.

2. Mimi_x3

do you know the product rule

3. TechnoFiction

Yeah, I somehow worked out the problem by myself. Just want to make sure if I got it right or not.

4. Mimi_x3

well tell me what you got :)

5. TechnoFiction

I look really ridiculous, but: $11x ^{10}e ^{x}+x ^{11}e ^{x}$ Here you go.

6. Mimi_x3

looks right to me

7. TechnoFiction

hm....ok, if you say so. I just don't feel right somehow. It look too long and weird.

8. Mimi_x3

It's right! $$u=x^{11} => u' = 11x^{10}$$ $$v=e^{x} => v' = e^{x}$$ $$=> 11x^{10}*e^{x}+ x^{11}e^{x}$$

9. Mimi_x3

You can also write it like: $$e^{x} (11x^{10}+x^{11})$$ if it looks too "weird" :)

10. TechnoFiction

ok, thanks :D

11. calculusfunctions

You could also factor the $x ^{10}$and express the derivative as$\frac{ dy }{ dx }=x ^{10}e ^{x}(11+x)$

12. TechnoFiction

Cool, thanks