Product/Quotient/Power 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 f(x) = 3x³ - x - 1, find f'(2)

• 35
• 18
• 17
• 12

Tags

CCSS.HSF.IF.A.2

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

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

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

Tags

CCSS.HSF.IF.A.2

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

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

Derivative means the same thing as

• slope of the tangent line
• slope of the normal line
• exponent
• slope of the secant line

Given f (x) = 5sinx + 3x³cosx, f '(x) =

• -5cosx − 3x³sinx + 9x²cosx
• 5sinx − 3x³sinx + 9x²cosx
• 5cosx − 3x³sinx + 9x²cosx
• 5cosx + 3x³sinx + 9x²cosx

How do you find horizontal tangent lines?

• Find where the derivative is undefined
• Find where the derivative equals zero
• Find where the derivative is 1
• Find where the derivative is negative

• cscx cotx
• secx tanx
• sec²x
• -cscx cotx

Tags

CCSS.HSF.TF.C.8