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

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

   Hint (a):

   Use both the Chain and Product Rule.

2. $3xy − x^2 = 2$

   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):

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

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

   Hint (c):

   Solve for y first.