chain rule related rates implicit

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

• 6 -x
• 3x² +3y² 
• −x²/y²
• 0

Find dy/dx at a given point.

• 5/4
• 4/5
• 1
• -5

• A

• B

• C

• D

Tags

CCSS.HSA.SSE.A.2

CCSS.HSN.RN.A.2

• A

• B

• C

• D

• E

Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The radius of the spill increases at a rate of 5 m/min. How fast is the area of the spill increasing when the radius is 5 m?

• 50π m²/min

• 47π m²/min

• 52π m²/min

• 40π m²/min

Tags

CCSS.7.G.B.4

A 5 ft ladder is leaning against a wall and sliding towards the floor. The top of the ladder is sliding down the wall at a rate of 2 ft/sec. How fast is the base of the ladder sliding away from the wall when the base of the ladder is 3 ft from the wall?

• 4/3 ft/sec

• 8/7 ft/sec

• 1 ft/sec

• 8/3 ft/sec

Tags

CCSS.8.G.B.8

Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 4 cm/min. How fast is the area of the pool increasing when the radius is 10 cm?

• 86π cm²/min

• 89π cm²/min

• 80π cm²/min

• 71π cm²/min

Tags

CCSS.7.G.B.4

Find  $\frac{dv}{dt}\ if\ v=t+\frac{8}{t}$  

•  $1-\frac{8}{t^2}$  

•  $1-\frac{8}{t}$  

•  $t-\frac{8}{t^2}$  

•  $1+\frac{8}{t^2}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Find  $\frac{dy}{dx}\ if\ y=\frac{x^3}{x-1}$  

•  $\frac{2x^3-3x^2}{\left(x-1\right)^2}$  

•  $\frac{2x^3+3x^2}{\left(x-1\right)^2}$  

•  $\frac{-2x^3-3x^2}{\left(x-1\right)^2}$  

•  $\frac{-2x^3+3x^2}{\left(x-1\right)^2}$  

Tags

CCSS.HSA.APR.D.6

Find the derivative of y = 2x² (3x - 4)

• 6x³ - 8x²
• 18x² - 16x
• 15x² - 6x
• 6x - 4