Question

Harder differentiation: ROUND 2. Differentiate the following function ;)

Answer 1

\[y=\ln(e ^{-x} + xe ^{-x})\]

Answer 2

In the illustrious words of @satellite73 .....Euler

Answer 3

euler?

Answer 4

\[\frac{d}{dx}[\ln(f(x)]=\frac{f'(x)}{f(x)}\]

Answer 5

I know how to solve it. :)

Answer 6

I know how to solve it. :)

Answer 7

just curious, what language is euler?

Answer 8

\[\huge y'=\frac{ d }{ dx }(\ln(e ^{-x}+\frac{ x }{ e^x })\]

\[\huge y' = \frac{ \frac{ d }{ dx }(e ^{-x}+\frac{ x }{ e^x } }{ e ^{-x}+e ^{-x}x }\]

\[\huge y' =- \frac{ x }{ e^x \left( e ^{-x}+\frac{ x }{ e^x } \right) }\]

I skipped a lot of steps because I'm too lazy to right everything out..would take too long.

Answer 9

Unfortunately, I have found a different answer

Answer 10

Let me guess, y' = -x/(x+1)

Answer 11

more like

Answer 12

\[\frac{ -xe ^{-x} }{ xe ^{-x} + e ^{-x}}\]

Answer 13

@iambatman

Answer 14

But A for effort!