Find the first partial derivatives of the function.

f$($x$,$ y$)=$ x$2$y $7$y$5$

Step $1$

We are asked to find the first partial derivatives of the following function.

f$($x$,$ y$)=$ x$2$y $7$y$5$

Recall that for a function of two variables, partial derivatives measure rate of change with respect to one variable while the other remains constant.

To find

fx$,$

regard y as a constant and differentiate

f$($x$,$ y$)$

with respect to x$.$ In other words, we treat the function as a function of x only and find the derivative as we normally would, using the usual properties of derivatives as follows.

fx$=$

$$x

$($x$2$y $7$y$5)=$y$$

$$x

$$

$$

$$x

$(7$y$5)=$y$$

$0=$