Implicit Differentiation

Find $\frac{dy}{dx}$  if:  $x^2+y^2=4$   

•  $\frac{dy}{dx}=-\frac{x}{y}$  

•  $\frac{dy}{dx}=\frac{x}{y}$  

•  $\frac{dy}{dx}=-x$  

•  $\frac{dy}{dx}=-y$  

Find $\frac{dy}{dx}$  if:  $y-2xy=3x$   

•  $\frac{dy}{dx}=\frac{3+2y}{1-2x}$  

•  $\frac{dy}{dx}=\frac{3+2y}{2x-1}$  

•  $\frac{dy}{dx}=\frac{2y+3}{2x+1}$  

•  $\frac{dy}{dx}=\frac{2y}{1-2x}$  

Find $\frac{dy}{dx}$  if:  $x=\sin\left(xy\right)$   

•  $\frac{dy}{dx}=\frac{\sec\left(xy\right)-y}{x}$  

•  $\frac{dy}{dx}=\frac{\sec\left(xy\right)-x}{y}$  

•  $\frac{dy}{dx}=\frac{y-\sec\left(xy\right)}{x}$  

•  $\frac{dy}{dx}=\frac{x-\sec\left(xy\right)}{y}$  

Find $\frac{d^2y}{dx^2}$  if:  $x^2-y^2=8$   

•  $\frac{d^2y}{dx^2}=\frac{-8}{y^3}$  

•  $\frac{d^2y}{dx^2}=\frac{8}{y^3}$  

•  $\frac{d^2y}{dx^2}=\frac{-8}{y^2}$  

•  $\frac{d^2y}{dx^2}=\frac{8}{y^2}$