# Compute the derivatives indicated. f(x,y)=3x^{2}y-6xy^{4}, \frac{\partial

Compute the derivatives indicated.
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Step 1
Here given as
$f\left(x,y\right)=3{x}^{2}y-6x{y}^{4}$
Now
$\frac{\partial f}{\partial x}=\frac{\partial }{\partial x}\left(3{x}^{2}y-6x{y}^{4}\right)$
$=\left(6xy-6{y}^{4}\right)$
$\frac{{\partial }^{2}f}{\partial {x}^{2}}=\frac{\partial }{\partial x}\left(6xy-6{y}^{4}\right)$
$⇒\frac{{\partial }^{2}f}{\partial {x}^{2}}=6y$
Step 2
Thus
$\frac{\partial f}{\partial y}=\frac{\partial }{\partial y}\left(3{x}^{2}y-6x{y}^{4}\right)$
$=\left(3{x}^{2}-24x{y}^{3}\right)$
$\frac{{\partial }^{2}f}{\partial {y}^{2}}=\frac{\partial }{\partial y}\left(3{x}^{2}-24x{y}^{3}\right)$
$⇒\frac{{\partial }^{2}f}{\partial {y}^{2}}-62x{y}^{2}$