Given the transformation u=y-lnx and v=y-x+1 ... Calculate the partial derivatives dy/dv and dx/du

Question

anonymous · Answer

If you mean $\frac{\partial y}{\partial v}$ and $\frac{\partial x}{\partial u}$, then you need to solve the system of equations for explicit equations for $y$ and $x$  in terms of $u$ and $v$, and then just find the partials as you always would.

anonymous · Answer

can you write the equations please ? i don't really get it ..

hartnn · Answer

since u are finding partial derivative of v w.r.t y
u treat x as constant in v=y-x+1
so now when u diff w.r.t y what u get??

anonymous · Answer

i have du = dy -dx(1/x) and dv = dy - dx ... but how do i proceed ?

hartnn · Answer

but i told u x is constant in v=y-x+1
so dv/dy is just 1

anonymous · Answer

alright .. i get it so i have dv/dy =1 and how do i get dx/du ?

hartnn · Answer

treat y as constant in u=y-ln x

anonymous · Answer

Thanks ! but how do you know that you should treat x and y as constants each time ?

hartnn · Answer

because of the word 'partial'
the only variable would be the one u are diff with.

anonymous · Answer

!!! thank you !!

hartnn · Answer

welcome :)