Question $10(4$ points$)$

Find all the first order partial derivatives for the following function.

$f(x,y,z)=cosxsi{n}^{2}yz$

$\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{x}}=sinxsi{n}^{2}yz$;$\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{y}}=-cosxsinyzcosyz$;$\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{z}}=-cosxsinyzcosyz$

$\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{x}}=sinxsi{n}^{2}yz$;$\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{y}}=-2zcosxsinyzcosyz$;$\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{z}}=-2ycosxsinyzcosyz$

$\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{x}}=-sinxsi{n}^{2}yz$;$\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{y}}=2zcosxsinyzcosyz$;$\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{z}}=2ycosxsinyzcosyz$

$\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{x}}=-sinxsi{n}^{2}yz$;$\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{y}}=zcosxsinyzcosyz$;$\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{z}}=ycosxsinyzcosyz$