### Home > APCALC > Chapter 6 > Lesson 6.2.1 > Problem6-59

6-59.

For each of the following equations, what is $\frac { d y } { d x }$?

1. $y = x ^ { 3 } \operatorname { sin } ( \operatorname { cos } ( x ) )$

Use both the Chain and Product Rule.

1. $3 x y - x ^ { 2 } = 2$

Before you differentiate, you could solve for $y$.
Or, you could use implicit differentiation:

$\frac{d}{dx}(3xy-x^{2})=\frac{d}{dx}(2)$

$3y\left (\frac{dx}{dx} \right )+3x\left ( \frac{dy}{dx} \right )-2x\left ( \frac{dx}{dx} \right )=0$

$\text{Note: }\left ( \frac{dx}{dx} \right )=1$

$\text{Solve for }\left ( \frac{dy}{dx} \right ).$

1. $\quad \frac { 1 } { y } = x$

Solve for $y$ first.