Derivative rules

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

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

Which of the following is the derivative of g(x)= (x²)(2x⁴ + 2)⁵ ?

• g^'(x)= (2x)(2x⁴ + 2) ⁵ + (x²)(5(2x⁴ + 2)⁴(8x³))

• g^'(x)= 2x + 8x³

• g^'(x)= (2x)(2x⁴ + 2)⁵ + (x²)(8x³)

• g^'(x)= (2x)(5(2x⁴ + 2)⁵(8x³)) + (x²)(2x⁴ + 2)

Tags

CCSS.HSA.SSE.A.2

Which of the following is the derivative of the function h(t) = t⁴ - (t⁴ - 1)⁸ ?

• h^'(t)= 4t³ - 8t³(t⁴ - 1)⁸

• h^'(t)= 4t³ - 32t³(t⁴ - 1)⁷

• h^'(t)= 4t³ - 8(t⁴ - 1)⁷

• h^'(t)= 4t² - 32t³(t⁴ - 1)⁸

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

At which point(s) will the slopes of the tangent line are zero?

• at C only

• at points A, C and E only

• at point B and D only

• at points A and E only

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

What is the derivative of f?

• 1/(x - 1)^-1

• -1/(x - 1)^-2

• -1/(x - 1)

• -1/(x - 1)²

Tags

CCSS.HSA.APR.D.7

Let f(x) = 2x - 1 and g(x) = x². If y = f[g(x)], then what is y’?

• 2x

• 4x

• 2x - 1

• 2(2x - 1)

Tags

CCSS.HSF-BF.A.1C

What is the derivative of tan(x)?

• -sec²(x)
• -csc²(x)
• sec²(x)
• csc²(x)

What is the derivative of cot(x)?

• sec²(x)
• -sec²(x)
• csc²(x)
• -csc²(x)

Set up the derivative of y=(3x⁴ - 7)*(5x² + 1)

• (12x³)*(10x)
• (3x⁴ - 7)*(10x) + (12x³)*(5x² + 1)
• (3x⁴ - 7)*(10x) - (12x³)*(5x² + 1)
• (3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

Tags

CCSS.HSA.APR.A.1

Differentiate f(x) = (9 - 4x²)^-1

• 8x/(9 - 4x²)^-2

• 8x/(9 - 4x²)²

• -8x/(9 - 4x²)^-2

• -8x(9 - 4x²)²