Partial Derivatives. For each of the following multi$-$variable functions, compute the partial derivatives with respect to both x and y$.$a$.$ f$($x$,$ y$)=$ xybcif$($x$,$ y$)=2$x$+3$yf$($x$,$y$)=$ry$*$d$.$ f$($x; y$)=$ Inx$+21$n ye$.$ f$($x$,$ y$)=2$V$++2/11.$ J$5,3=$g$.$ f$($x$,$y$)=$ L$2$A Canonical Utility Function. Consider the utility functionc$\backslash$deg $-12($C$)=-1-0$where c denotes consumption of some arbitrary good and a $($the Greek letter"sigma"$)$ is known as the "curvature parameter" because its value governs how curved the utility function is$.$ In the following, restrict your attention to the region c $>0($because "negative consumption" is an ill$-$defined concept$).$ The parameter o is treated as a constant.a$.$ Plot the utility function for o $=0.$ Does this utility function display diminishingmarginal utility? Is marginal utility ever negative for this utility function?b$.$ Plot the utility function for o $=1/2.$ Does this utility function display diminishing marginal utility? Is marginal utility ever negative for this utility function?