Differentiation Rules 4

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

• 6 -x
• 3x² +3y² 
• −x²/y²
• 0

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

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

Find dy/dx by Implicit Differentiation 
8x² + 16y² = 144

• x /2y
• x² / y
• −x /2y
• x² / y²

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 dy/dx for 
y = (x² + 1)³

• dy/dx = 3(x² + 1)²
• dy/dx = 3(2x)²
• dy/dx = 6x(x² + 1)²
• dy/dx = 2x(x² + 1)²

What is the derivative of tan y  with respect to x?

• sec y (dy/dx)
• sec²y (dy/dx)
• tan²y (dy/dx)
• sec²y

Find the derivative of  f(x) = (x⁶ + 4)⁵

• f '(x) = 5x⁵(x⁴ + 4)⁴
• f '(x) = 6x⁵(x⁶ + 4)⁴
• f '(x) = 30x⁵(x⁶ + 4)⁴
• f '(x) = 30x⁶(x⁶ + 4)⁴

If  $x^2+y^2=25$  what is the value of  $\frac{d^2y}{dx^2}$  at the point  $\left(4,3\right)$  ?

•  $-\frac{25}{27}$  

•  $-\frac{7}{27}$  

•  $\frac{7}{27}$  

•  $\frac{3}{4}$  

•  $\frac{25}{27}$  

Given the position function, find the velocity at t=2

• 96
• 40
• 28
• 36

Given the position function, find the acceleration at t=6

• -6
• -10
• 12
• -20