Let $ w = f(x-y,y-z,z-x)$. Show that $ \frac{\partial w}{\partial x} + \frac{\partial w}{\partial y} + \frac{\partial w}{\partial z} = 0$
I wouldn't have problem, if it was written in $f(x,y,z) = x^2 + y^3 + z^4$ or something similar. Can I ask for little help what to start with?
Thank you!
I'll show you how to compute the first partial derivative; you can do the others to finish the problem. As Martín-Blas Pérez Pinilla said, use the multivariable chain rule: \begin{align} \frac{\partial w}{\partial x} &= \frac{\partial f}{\partial x}\cdot\frac{\partial}{\partial x}(x-y) + \frac{\partial f}{\partial y}\cdot\frac{\partial}{\partial x}(y-z) + \frac{\partial f}{\partial z}\cdot\frac{\partial}{\partial x}(z-x) \\ &= \frac{\partial f}{\partial x} - \frac{\partial f}{\partial z}. \end{align}