# Find the partial derivatives of  u=xlny+ylnz+zlnx  ?

May 12, 2017

We have:

$u = x \ln y + y \ln z + z \ln x$

Remember when partially differentiating that we differentiate wrt the variable in question whilst treating the other variables as constant. And so the partial derivatives are:

$\frac{\partial u}{\partial x} = {u}_{x} = \ln y + \frac{z}{x}$

$\frac{\partial u}{\partial y} = {u}_{y} = \frac{x}{y} + \ln z$

$\frac{\partial u}{\partial z} = {u}_{z} = \frac{y}{z} + \ln x$