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2.8 Partial differentiation in more than two variables

We can carry out the same procedure for a function of more than two variables.

Let $f(x,y,z)=x^{2}+xyz^{2}$ be a function of three variables. Find its partial derivatives.

Solution. We have

\frac{\partial f}{\partial x}=\,{2x+yz^{2},}\;\;\frac{\partial f}{\partial y}=% \,{xz^{2},}\;\;\mbox{and}

\frac{\partial f}{\partial z}=\,{2xyz.}