SCalcET$914\mathrm{.}5\mathrm{.}058.$

A function f is called homogeneous of degree n if it satisfies the equation

f$($tx$,$ ty$)=$ tnf$($x$,$ y$)$

for all t$,$ where n is a positive integer and f has continuous second$-$order partial derivatives.

If f is homogeneous of degree n$,$ show that

fx$($tx$,$ ty$)=$ tn $1$fx$($x$,$ y$).$