Chain Rule Practice

Find dy/dx for 
y = (x² + 1)³

• dy/dx = 3(x² + 1)²
• dy/dx = 3(2x)²
• dy/dx = 6x(x² + 1)²
• dy/dx = 2x(x² + 1)²

Tags

CCSS.HSF-BF.B.4A

d/dx (sin³(4x^-6)) = ?

• -24x^-5 ⋅ cos (4x^-6) ⋅ 3sin²(4x^-6)
• -24x^-7 ⋅ cos (4x^-6) ⋅ 3sin²(4x^-6)
• -24x^-7 ⋅ 3cos²(4x^-6)
• 3cos²(-24x^-5)

• A or E
• B
• C
• D

Tags

CCSS.HSA.REI.D.10

• A
• B
• C
• D

• 
• 
• 
• 

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.1

CCSS.HSA.SSE.A.2

Differentiate:
f(x) = x⁷ (5 + 8x)³

• f '(x) = x² (5 + 8x)⁶ (35 + 80x)
• f '(x) = x⁶ (5 + 8x)² (35 + 80x)
• f '(x) = 8x⁷ (5 + 8x)² (35 + 80x)
• f '(x) = x⁶ (5 + 8x)³ (35 + 80x)

• 
• 
• 
• 

Using the data in the chart, find the value of d/dx [g(f(x))] at x = 9

• -6+2π
• -3π
• 8+(3π)/2
• (-3π)/2

.

• (3x²-2)cos(x³-2x)

• -(3x²-2)cos(x³-2x)

• cos(2x²-2)

• sin(2x²-2)

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)