Find $\displaystyle f_{(xy)}$ for $\displaystyle f(x,y)=\frac{4x^2}{y}+\frac{y^2}{2x}$
I did one with $\displaystyle f_{x}(x,y)\ for\ f(x,y)=e^{xy}(cos x\ sin x)$
and got $\displaystyle e^{xy}(sin x\ siny) $
Thanks
$\displaystyle f=\frac{4x^2}{y}+\frac{y^2}{2x}$
$\displaystyle f=4x^2y^{-1}+\frac{y^2x^{-1}}{2}$
Take derivative w.r.t $\displaystyle x$ of $\displaystyle f$
$\displaystyle f_x=8xy^{-1}+\frac{-y^2x^{-2}}{2}$
$\displaystyle f_x=8xy^{-1}+\frac{-y^2x^{-2}}{2}$
Take derivative w.r.t $\displaystyle y$ of $\displaystyle f_x$
$\displaystyle f_{xy}=-8xy^{-2}+\frac{-2yx^{-2}}{2}$
Anygood?