Hy all, i will take $x\in \mathbb R$ and $y\in\mathbb R^n$.
I wondering about what happen if i have $\partial_{x}u(e^{-x},y)$ and i do variable change $s=e^{-x}$. How is change $\partial_{x}u(e^{-x},y)$?
The new function is just $\partial_{s}u(s,y)$? or i need take $-\log(s)=x$ and do the calculation $$ds=-e^{-x}dx\leftrightarrow -\frac{ds}{s}=dx$$ and work more, sorry i am really stuck and i do not know how continuous, please can you help me?
$\partial_{x}u(e^{-x},y)=-\frac{\partial_s u(s,y)}{s}?$