- #1
Vagrant
- 195
- 1
Homework Statement
I found this solved example in an old textbook. I don't think that the solution provided is correct. I'll be very grateful if someone could verify it.
Question:
xxyyzz = c
What is [itex]\frac{∂z}{∂x}[/itex]?
Solution Provided:
Taking logarithms on both sides:
zlog(z) = log(c) - xlog(x) - ylog(y)
Differentiating w.r.t. x
[itex](z.\frac{1}{z}+ log(z))\frac{∂z}{∂x} = -(x.\frac{1}{x} + 1.log(x))[/itex]
Homework Equations
The Attempt at a Solution
Isn't this solution missing a [itex]\frac{∂y}{∂x}[/itex] term as:
[itex](z.\frac{1}{z}+ log(z))\frac{∂z}{∂x} = -(x.\frac{1}{x} + 1.log(x)) - (y.\frac{1}{y} + 1.log(y))\frac{∂y}{∂x}[/itex]
Thanks.