AP Calc AB Review for QZ 11-12

Find $\frac{dy}{dx}$ at the point $\left(2,3\right)$ for

$x^3+2xy-y^2=11$ .

• $-\frac{4}{7}$

• 12

• -9

• 9

Tags

implicit differentiation

Find $\frac{dy}{dx}$ for $x^3+y^3=36$ .

• $6-x$

• $3x^2+3y^2$

• $-\frac{x^2}{y^2}$

• 0

Tags

implicit differentiation

Find  $\frac{dy}{dx}$  for  $xy+y^2=2$ . 

•  $-\frac{y}{x+2y}$  

•  $\frac{y}{x+2y}$  

•  $-\frac{3y}{x}$ 

•  $-\frac{3x}{y}$ 

Find $\frac{\text{d}y}{\text{d}x}$ for $\sin\ \left(x^2y^2\right)=x$

• $\frac{1}{2x^2y\ \cos\left(x^2y^2\right)}-\frac{2y}{x}$

• $\frac{2}{2x^2y^2\cos\ \left(x^2y^2\right)}-\frac{y}{x}$

• $\frac{1}{2x^2y\cos\left(x^2y^2\right)}-\frac{y}{x}$

• None of the above.

Tags

implicit differentiation

trig differentiation