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\newcommand\ds{\displaystyle}
\begin{document}

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QUESTION

If $f(x,y)=xy+y^3+x^2y\sin y$ determine $\ds\frac{\partial
f}{\partial x}$ and $\ds\frac{\partial f}{\partial y}$.

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ANSWER

$\ds f(x,y)=xy+y^3+x^2y\sin y\\ \frac{\partial f}{\partial x}
=y+2xy\sin y,\hspace{1cm}\frac{\partial f}{\partial y}
=x+3y^2+x^2(y\cos y+\sin y)$





\end{document}