Find

dydx

by implicit differentiation.

y cos$($x$)=9$x$2+8$y$2$

Step $1$

Recall that the method of implicit differentiation consists of differentiating both sides of an equation with respect to x and then solving the resulting equation for

dydx

$.$

We begin by differentiating both sides of the given equation

y cos$($x$)=9$x$2+8$y$2.$

The beginning of this process proceeds as follows, using the sum rule and the constant rule on the right side of the equation.

ddx

$($y cos$($x$))=$

ddx

$(9$x$2+8$y$2)$

ddx

$($y cos$($x$))=$

ddx

$(9$x$2)+$

ddx

$$

$$

ddx

$($y cos$($x$))=9$

ddx

$($x$2)+8$

ddx

$$