Differentiate y(e^y)

[rhino4552]

I need to differentiate y(e^y). I am using separation of variables on a larger problem, but I cannot figure out how to differentiate this. This is the only step in the problem I am having trouble with. Thank you in advance.

 

[galactus]

This is not a DE. No separation of variables. Use the product rule

\(\displaystyle \frac{d}{dy}[ye^{y}]=ye^{y}+e^{y}(1)=e^{y}(y+1)\)

 

[rhino4552]

I am sorry, I meant to say integrate, not differentiate. Thank you for the input.

 

[Deleted member 4993]

I am sorry, I meant to say integrate, not differentiate. Thank you for the input.

Use integration by parts:

\(\displaystyle \int u dv \ = \ uv - \int v du\)

in your case u = y and dv = e[sup:2beob4wb]y[/sup:2beob4wb]dy

.

 

[rhino4552]

Ok, I see. Thank you. I had the u a something different.