Product and Quotient Rule

Given that y = (x+2)/(x-3), find y'.

• y' = -1/(x-3)²
• y' = -5/(x-3)²
• y' = (2x-5)/(x-3)²
• y' = (2x-1)/(x-3)²

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

• 51
• 12
• 9
• 6

Tags

CCSS.HSF.IF.A.2

CCSS.HSN.VM.A.3

Given that f(x) = 3x³ - x - 1, find f'(2)

• 35
• 18
• 17
• 12

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

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

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

Find f'(x) if       
f(x)=(2x-7)/(x+3) 

• 2
• 13/(x+3)²
• -4/(x+3)²
• -13/(x+3)

Tags

CCSS.HSA.APR.D.7

Find f''(1) if
f(x)=(x²-2x-1)/(3x)

• -2/3
• 2/3
• 4/3
• -4/3