anonymous
  • anonymous
Can anyone help me with the derivative of: y=x^11 e^x
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
\[y=x ^{11}e ^{x}\] Much easier to look at.
Mimi_x3
  • Mimi_x3
do you know the product rule
anonymous
  • anonymous
Yeah, I somehow worked out the problem by myself. Just want to make sure if I got it right or not.

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Mimi_x3
  • Mimi_x3
well tell me what you got :)
anonymous
  • anonymous
I look really ridiculous, but: \[11x ^{10}e ^{x}+x ^{11}e ^{x}\] Here you go.
Mimi_x3
  • Mimi_x3
looks right to me
anonymous
  • anonymous
hm....ok, if you say so. I just don't feel right somehow. It look too long and weird.
Mimi_x3
  • Mimi_x3
It's right! \(u=x^{11} => u' = 11x^{10}\) \(v=e^{x} => v' = e^{x}\) \(=> 11x^{10}*e^{x}+ x^{11}e^{x}\)
Mimi_x3
  • Mimi_x3
You can also write it like: \(e^{x} (11x^{10}+x^{11})\) if it looks too "weird" :)
anonymous
  • anonymous
ok, thanks :D
calculusfunctions
  • calculusfunctions
You could also factor the \[x ^{10}\]and express the derivative as\[\frac{ dy }{ dx }=x ^{10}e ^{x}(11+x)\]
anonymous
  • anonymous
Cool, thanks

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