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

6-59.

For each of the following equations, find $\frac { d y } { d x }$ .

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

Use both the Chain and Product Rule.

2. $3xy − x^2 = 2$

Before you differentiate, you could solve for y.
Or, you could use implicit differentiation:
$\frac{d}{dx}(3xy-x^{2})=\frac{d}{dx}(2)$
$3y\left (\frac{dx}{dx} \right )+3x\left ( \frac{dy}{dx} \right )-2x\left ( \frac{dx}{dx} \right )=0$
$\text{Note: }\left ( \frac{dx}{dx} \right )=1$

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

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

Solve for y first.