TuringTest
Let\[y=x^p(1+x)^q\]find\[y^{(p+q)}\]



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TuringTest
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that's the (p+q)th derivative by the way
Sorry that I have to go soon, but I look forward to seeing your responses when I return.

amistre64
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ln(y) = ln(x^p) + ln(1+x)^q
y'/y = p/x + q/(1+x)
hmm

joemath314159
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i think the answer is just (p+q)!

joemath314159
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since the highest power of x will be x^(p+q), and all the other powers of x will become 0 after P+q derivatives.

amistre64
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sounds plausible to me

TuringTest
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hint:(Leibniz' theorem/ binomial stuff)

TuringTest
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at least in MIT's solution
I'd like to see others

amistre64
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lol, id like to see mits solution :)

TuringTest
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I'll send it to you....

AccessDenied
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im curious, what class is this problem from?

TuringTest
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OCW calc I

AccessDenied
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Ahh, okay. Thank you. :)
