Question

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

Answer 1

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.

Answer 2

ln(y) = ln(x^p) + ln(1+x)^q

y'/y = p/x + q/(1+x)

hmm

Answer 3

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

Answer 4

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.

Answer 5

sounds plausible to me

Answer 6

hint:(Leibniz' theorem/ binomial stuff)

Answer 7

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

Answer 8

lol, id like to see mits solution :)

Answer 9

I'll send it to you....

Answer 10

im curious, what class is this problem from?

Answer 11

OCW calc I

Answer 12

Ahh, okay. Thank you. :)

Answer 13

http://en.wikipedia.org/wiki/Leibniz_rule_(generalized_product_rule)