CPM Homework Help : CALC Problem 6-59

For each of the following equations, find . Homework Help ✎
1. y = x³ sin(cos x)
2. 3xy − x² = 2

Hint (a):

Use both the Chain and Product Rule.

Hint (c):

Solve for y first.

Step 1(b):

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

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

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

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

Step 2(b):

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