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

• 35
• 18
• 17
• 12

Tags

CCSS.HSF.IF.A.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.HSF.IF.A.2

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

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

Find the derivative of g(x)=(3x-2)/(x²+2)

• 9x²+2
• 3(x²+2)/(x²+2)²
• (-3x²+4x +6)/(x²+2)²
• (-3x²+10)/(x²+2)²

• 8x⁴ -60x²
• 16x⁴
• (8x⁴ -60x²)/(2x²-5)²
• 3x

Tags

CCSS.HSF-IF.C.7D

Derivative means the same thing as

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

Which if the following is not a correct notation for 'derivative?'

• f'(x)
• y'
• dy
• dy/dx

Find the derivative.

y = 2 / (2x⁴ − 5)

• y ′ = -16x³ / (2x⁴-5)²

• y′ = 4x⁶ + 8x³ + 4

• y′ = 16x³ / (2x⁴ -5)

Find the derivative.
y = $4x^2-\frac{3}{x}\ +\sqrt{x}$  

•  $8x\ +\frac{3}{x^2}+\frac{1}{2\sqrt{x}}$ 

•  $8x\ +3\ +\frac{x}{2}$  

•  $8x\ +3x\ +\frac{1}{2}x$  

•  $8x\ +3x^{-1}+x^{\frac{1}{2}}$