IMPLICIT AND PARAMETRIC 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 the derivative:
y=5x²e^3x

• y'=10xe^3x(2x+3)
• y'=5xe^3x(3x+2)
• y'=10ex^3x(3x+2)
• y'=5xe^3x(2x+3)

Find the second derivative of f(x) = x² + e^x  - cosx

• f"(x) = 2 + e^x + cosx
• f"(x) = 2x + e^x + cosx
• f"(x) = 2x + xe^x - cosx
• f"(x) = 2x + e^x + sinx

Find dy/dx at the given point

x³ +2xy -y²=11 at (2,3)

• -4/7

• 12

• -9

• 9

Find   $\frac{dy}{dx}$  :  $2x^2-3y^2=4$  

•  $\frac{2x}{y}$  

•  $\frac{x}{3y}$  

•  $\frac{3y}{2x}$  

•  $\frac{2x}{3y}$  

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

•  $-\ \frac{2x}{1+3y^2}$  

•  $-\frac{x+3y^2}{2x+y}$  

•  $-\frac{2x+y}{x+3y^2}$  

•  $-\frac{2x}{x+3y^2}$  

Find the point based on the parametric equations. t = 3

x = 1 - 2t

y =4t + 1

• (-5, 13)

• (13, -5)

• (5, 13)

• (13, 5)

Find the ordered pair based on the parametric equations.

t = -2

x = t² - 2

y = -t + 2

• (2, 4)

• (4, 2)

• (-6, 0)

• (0,-6)

For $x=3t^2+1,\ y=t^3-2t^2$ , determine  $\frac{d^2y}{dx^2}$  in terms of t. 

•  $\frac{d^2y}{dx^2}=-\frac{1}{12t}$  

•  $\frac{d^2y}{dx^2}=\frac{1}{12}$  

•  $\frac{d^2y}{dx^2}=\frac{1}{12t}$  

•  $\frac{d^2y}{dx^2}=-\frac{1}{t}$