Quotient Rule

​Product and Quotient Rule

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Multiple Choice

Find the derivative of f(x) = 6x³⁰ -2x¹⁵ + 4x³ - 2x + 1. #3

• f'(x) = 18x²⁹ + 30x¹⁵ + 12x³ 
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² 
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² - 2
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² +1

Multiple Choice

What is the derivative of xⁿ? #5

• (n-1)xⁿ
• nxⁿ⁺¹
• (n+1)x^n-1
• nx^n-1

Multiple Choice

Find the derivative of the given equation
f(x) = x³ + x² + 3. #1

• 3x² + 2x
• 3x + 2x 
• 3x + 2x + 3
• x³ + x² 

Multiple Choice

Find the slope of f(x) = -3x²-6x at x = 1. #2

• m = 0
• f'(x) = -6x - 6
• f'(x) = 6x
• m = -12

Multiple Choice

The derivative of the given function is...#4

• y'=2x-x^-2
• y'=x^-1+8x
• y'=x^-2+8x
• y=8x-x^-2

Multiple Choice

Find the derivative of the given equation
f(x) = 7. #6

• 7
• 0
• 7x
• 14

Multiple Choice

Find the derivative of the given equation

f(x)=12-8x. #7

• -8x

• -8s

• -8

• 12 - 8

Multiple Choice

Use the product rule to determine the derivative. #8

• 4x⁸+60x⁶+12x³
• 12x⁷+36x²
• 32x⁷+36x²
• 20x⁶

Multiple Choice

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

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

Multiple Choice

Derivative means the same thing as...#10

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

Multiple Choice

What is the derivative? #11

• -20x⁶ + 10x
• -70x⁶ + 30x⁴ + 10x
• 5x² + 10x - 3
• -10x⁷ - 94x⁵ + 5x² - 3

Multiple Choice

Which one is the product rule? #12

• f(x)g(x)
• f'(x)g(x)-f(x)g'(x)
• f'(x)g(x)+f(x)g'(x)
• f'(x)g'(x)+f'(x)g'(x)

Multiple Choice

What is the derivative of the function? #13

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

Multiple Choice

Find the derivative. #14
y = x² / (3x-1)

• y' = 9x² - 12
  y' = (3x-1) / (3x-1)²
• y' = (3x² - 2x) / (3x-1)²
• y' = (6x+1)² / 3