$\displaystyle \begin{array}\\\text{Given:}\\

z=sin(2u)cos(3v)\\

\text{find}\frac{\partial{z}}{\partial{u}}\\

\\

\\

\text{The answer is the following:}\\

\\

[sin(2u)(0)]+[cos(3v)(cos(2u)(2)]\\

\\

\text{however, i'm not sure why the answer doesn't simply regard the cos(3v) as a constant, making the answer:}\\

\\

[cos(3v)][cos(2u)(2)],\\

\\

\text{as in the problem:}\\

f(x,y,z)=x^{2}y^{5}+xz^{2}\;\;\;\text{where}\;\;f_ {x}=y^{5}2x+z^{2}(1).\\

\text{Here, }y^{5}\text{and }z^{2}\text{are treated as if they were constants.}\\

\\

\text{I suspect the chain rule has something to do with it, but i just don't know. Could someone help to clarify this?}

\end{array}$