Derivatives Quiz (Power, Product, and Quotient Rule)

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

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

• 8x⁴ +60x²/(2x²-5)²

• 16x⁴-60x²/(2x²-5)²

• (8x⁴ -60x²)/(2x²-5)²

• 3x

What is the derivative of csc(x)?

• csc(x)cot(x)
• -csc(x)cot(x)
• -csc²(x) 
• -cot²(x)

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

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

Tags

CCSS.HSA.APR.A.1

At which x-value is f continuous but not differentiable?

• a
• b
• c
• d

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

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

• m = 0

• f'(x) = -6x - 6

• f'(x) = 6x

• m = -12

What is the derivative of f(x) = 2x³ - 4x + 5?

• f'(x) = 6x² - 4x

• f'(x) = 2/3x² - 4x

• f'(x) = 3x² - 4

• f'(x) = 6x² - 4

Tags

CCSS.HSA.APR.A.1

CCSS.HSF.IF.A.2

f(x)= 5/x^{2
f'(x) =} 

• 5x
• 5/2x
• 5x^-2
• -10/x³

Find the derivative.

• x⁴ cosx - 4x³sinx
• x⁴ cosx + 4x³sinx
• 4x³cosx
• -4x³cosx

Tags

CCSS.HSA.APR.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.TF.A.2

CCSS.HSF.IF.A.1

Find the second derivative of
f(x) = x² + e^x  - cosx

• f"(x) = 2 + e^x + cosx
• f"(x) = 2x + e^x + cosx
• f"(x) = 2x + xe^x - cosx
• f"(x) = 2x + e^x + sinx