Question

Implicit Differentiation problem

Answer 1

Use implicit differentiation to find ∂z/∂x \[yz = 9ln(x+z)\]

Answer 2

I know y is treated as a constant, and I've found \[y\frac{dz}{dx}=\frac{9}{x+z}(1+\frac{dz}{dx})\] But, solving it I get \[\frac{9(x+z)^{-1}}{9(x+z)^{-1}-y}=\frac{dz}{dx}\]

Answer 3

But that apparently is wrong. I'm guessing it is an algebra error somewhere, but can't find it.