Question

Use implicit differentiation to find

dz/dy for yz = ln (x+z)

I am unsure of how to deal with the right side specifically.

Answer 1

Consider z as a function of y, and differentiate both sides with respect to y.

Is x supposed to be a constant on the right? Or did you mean to type "y" there? If x is another variable, z is not a fucntion of y alone, and you would have to deal with partial derivatives.

Answer 2

y dz/dy + z dy/dy = dz/dy /(x+z)

z = (dz/dy)(1/(x+z) - y)

z = (dz/dy) ( 1 -zx - xy)/(x+z)

dz/dy = (z^2 + xz)/(1 - xz - xy)

Answer 3

I assumed that partial is intended and x is constant for dz/dy