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



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TechnoFiction
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\[y=x ^{11}e ^{x}\] Much easier to look at.

Mimi_x3
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do you know the product rule

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

Mimi_x3
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well tell me what you got :)

TechnoFiction
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I look really ridiculous, but: \[11x ^{10}e ^{x}+x ^{11}e ^{x}\] Here you go.

Mimi_x3
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looks right to me

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

Mimi_x3
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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
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You can also write it like: \(e^{x} (11x^{10}+x^{11})\)
if it looks too "weird" :)

TechnoFiction
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ok, thanks :D

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

TechnoFiction
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Cool, thanks