Chain Rule Practice

Given f (x) =  − 3x³cosx

• 3x³cosx + 9x²sinx
•  − 3x³sinx + 9x²cosx
•   3x³sinx + 9x²cosx
•  3x³sinx − 9x²cosx

.

• (3x²-2)cos(x³-2x)

• -(3x²-2)cos(x³-2x)

• cos(2x²-2)

• sin(2x²-2)

What is f'(x) if f(x) = cos(5x⁴)?

• f'(x) = sin(20x³)
• f'(x) = 20x³ sin(5x⁴)
• f'(x) = -sin(20x³)
• f'(x) = -20x³ sin(5x⁴)

Find the derivative
f(t) = (t² + 2t)⁵

• f'(t) = 5(2t+2)⁴
• f'(t) = 5(t² + 2t)⁴
•  f'(t) = 5(t² + 2t)⁴(2t)
• f'(t) = 5(t² + 2t)⁴(2t + 2)

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

Find the derivative.

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

Tags

CCSS.HSA.APR.A.1

CCSS.HSF.TF.A.2

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)

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

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

Find the derivative of    f(x) = (x^6 + 4)^5

• f '(x) = 5x^5(x^4 + 4)^4
• f '(x) = 6x^5(x^6 + 4)^4
• f '(x) = 30x^5(x^6 + 4)
• f '(x) = 30x^6(x^6 + 4)

If y = f(g(x)) where y = (6x -5)⁴, choose u such that we can write y = f(u)

• -5⁴
• 6x - 5
• (6x - 5)4
• 6x

Tags

CCSS.HSF-BF.A.1C