Thread: Partial differentiation ln(x+y)=x

Hello guys,
wondering if anyone can help me out with this problem.
find dy/dx:
ln(x+y)=x

why is this solution invalid:
ln(x+y)=x
e^x=x+y
y=e^x-x
(dy/dx)=e^x-1

Many thanks.

I believe you meant to title your topic "Implicit differentiation..."

Your result is valid, it is just in a different form than that which is obtained by implicit differentiation.

Given then implicit differentiation yields:





Now, if we substitute for , we then find: