Implicit Differentiation

Find dy/dx by Implicit Differentiation 
x³ +y³  = 36

• 6 -x
• 3x² +3y² 
• −x²/y²
• 0

Find dy/dx
xy+y²=2

• -y/(x+2y)
• y/(x+2y)
• -3y/x
• -3x/y

Find dy/dx at a given point.

• 5/4
• 4/5
• 1
• -5

• -3
• 8
• 0
• 9

Find dy/dx at the given point

x³ +2xy -y²=11 at (2,3)

• -4/7

• 12

• -9

• 9

Find the derivative of  $x^2+xy+y^3=0$  

•  $-\ \frac{2x}{1+3y^2}$  

•  $-\frac{x+3y^2}{2x+y}$  

•  $-\frac{2x+y}{x+3y^2}$  

•  $-\frac{2x}{x+3y^2}$  

Using Implicit Differentiation, find  $\frac{\text{d}y}{\text{d}x}$ for  $\sin\ \left(x^2y^2\right)=x$ 

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

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

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

Find dy/dx by Implicit Differentiation
2xy³ - x²y = 2

• 2xy - 2y³
• 2y(x-y²)/x(6y²-x)
• -2y/x
• 2

Use implicit differentiation to find y' for the following equation:   4x cos(y) = 1

• y' = cos(y) / x sin(y)
• y' = 4x sin(y)
• y' = cot(y)
• y' = 4 / sec(y)tan(y)

 $-3\sin x+4\cos y=10$ 

Differentiate w.r.t x 

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

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

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

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