Implicit differentiation & related rates

-y/(x+2y)

y/(x+2y)

-3y/x

-3x/y

$$\frac{5}{y}$$  

$$\frac{10}{y}$$  

$$\frac{y^2}{5}$$  

$$\frac{y^2}{10}$$  

$$\frac{2x}{y}$$  

$$\frac{x}{3y}$$  

$$\frac{3y}{2x}$$  

$$\frac{2x}{3y}$$  

$$-\ \frac{2x}{1+3y^2}$$  

$$-\frac{x+3y^2}{2x+y}$$  

$$-\frac{2x+y}{x+3y^2}$$  

$$-\frac{2x}{x+3y^2}$$  

$$y=4\ x-9$$

$$x^{\ 2}+y^{\ 2}=49$$

$$x\ y=16$$

$$y=\sqrt{36-x^{\ 2}}$$

$$y=\frac{25\ x}{x^{\ 2}-64}$$

$$\frac{dy}{dx}=-\frac{2y}{3x}$$  

$$\frac{dy}{dx}=-\frac{2x}{3y}$$  

$$\frac{dy}{dx}=\frac{2y}{3x}$$  

$$\frac{dy}{dx}=-\frac{3x}{2y}$$  

$$\frac{dy}{dx}=-\frac{3\cos\left(x\right)}{4\sin\left(y\right)}$$  

$$\frac{dy}{dx}=\frac{3\cos\left(x\right)}{4\sin\left(y\right)}$$  

$$\frac{dy}{dx}=-\frac{3\cos\left(y\right)}{4\sin\left(x\right)}$$  

$$\frac{dy}{dx}=\frac{3\cos\left(y\right)}{4\sin\left(x\right)}$$