Required Review: Calculus

Find the derivative f(x) = (x² + 2x)⁵

• f'(x) = 5(2x+2)⁴
• f'(x) = 5(x² + 2x)⁴
•  f'(x) = 5(x² + 2x)⁴(2x)
• f'(x) = 5(x² + 2x)⁴(2x + 2)

Tags

CCSS.HSF.IF.C.8

What is the quotient rule for the derivative of f = u/v?

• f' = (vu' - uv')/v²
• f' = (uv' - vu')/v²
• f' = (vu' - uv')/u²
• f' = (uv' - vu')/u²

What is the product rule for the derivative of f = u⋅v?

• f' = u'v + uv'
• f' = uv' - vu'
• f' = u'u + v'v
• f' = v'u' - vu

Given that the position function for a particular object is given by 
s(t) = t³ - 3t +5, find the acceleration of the object at t = 2 seconds. 

• 27
• 12
• 6
• -2

A particle's speed is decreasing if

• it's acceleration is positive
• it's velocity is positive
• it's velocity and acceleration have the same sign
• it's velocity and acceleration have different signs

An objects distance from its starting point at time t is given by the equation
s(t) = t³ - 6t²  - 4. 
What is the speed of the object when its acceleration is 0? 

• 2
• -24
• 22
• 44

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.SSE.A.1

Find the derivative of f(x) = x²sinx

• f'(x) = 2xsinx - x²cosx
• f'(x) = 2xsinx + x²sinx
• f'(x) = 2xsinx + x²cosx
• f'(x) = 2xcosx

The equation of the tangent to y=1/x at x=3 is

• y=-1/9x+2/3
• y=1/3x+1/3
• y=1/9x+9
• y=1/9x

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Find dy/dx

• A

• B

• C

• D

Find the derivative:
y=e^5x

• y'=e^5x
• y'=5e^5x
• y'=5e^x
• y'=(1/5)e^5x