Question

How do i calculate the second derivative of...?

Answer 1

\[\left( x+1 \right)^{2}e ^{f(x)}\]

Answer 2

put the given function equals to y

Answer 3

take log on both sides.

Answer 4

now do the further process

Answer 5

Y'=\[2(x+1)e ^{f(x)}+(x+1)^{2}f'(x)e ^{f(x)}\]

Answer 6

y''=\[2e ^{f(x)}+2(x+1)f'(x)e ^{f(x)}+\]

Answer 7

How do I do the derivative of the last member of derivative one?

Answer 8

@SolomonZelman Professor Please help us

Answer 9

Say you have \(g(x) = h(x)~j(x)~k(x)\)
So for product rule of three functions or more:
\(g'(x) = h'(x)~j(x)~k(x)+h(x)~j'(x)~k(x)+h(x)~j(x)~k'(x)\)

Answer 10

greeky is here, idk how to do this question, not that good at math -:(

Answer 11

it's ok Professor of Mathematics. No worries.

Answer 12

"proffesor" is anyone who answers easy question to get 3000 badges? hehe openstudy.
I wish I learned this, then I would have been helpful, but only this comming year I will be able to do those.

Answer 13

So for last member, you have \( \dfrac{d}{dx}\left((x+1)^2f'(x)e^{f(x)}\right)\\ =\dfrac{d}{dx}\left[ (x+1)^2\right]f'(x)e^{f(x)}\\~~~~~~+(x+1)^2\dfrac{d}{dx}\left[f'(x)\right]e^{f(x)}\\~~~~~~+(x+1)^2f'(x)\dfrac{d}{dx}\left[e^{f(x)}\right]\)

Sorry for so messy looks but hope this helps

Answer 14

Thank you ^^