The Chain Rule

Find the derivative of  f(x) = (x⁶ + 4)⁵

• f '(x) = 5x⁵(x⁴ + 4)⁴
• f '(x) = 6x⁵(x⁶ + 4)⁴
• f '(x) = 30x⁵(x⁶ + 4)⁴
• f '(x) = 30x⁶(x⁶ + 4)⁴

Find the derivative of f(x)=(x³-2x)²

• 6x⁵ - 12x³+8x
• 6x⁵ - 16x³+8x
• x⁶-4x⁴+4x²
• 6x⁵ - 16x^3-8x

Tags

CCSS.HSA.APR.A.1

• A

• B

• C

• D

Tags

CCSS.HSA.SSE.A.2

CCSS.HSN.RN.A.2

• A

• B

• C

• D

• E

• 19.79898987

• 16.97056275

• 13.85640646

• 28.28427125

Tags

CCSS.HSA.REI.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)

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• 
• 

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.A.1

• 
• 
• 
• 

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.A.1

CCSS.HSA.SSE.B.3

Differentiate (2x + 2)(x - 5)⁸ with respect to x.

• (2x + 2)(x - 5)⁷ + 2(x - 5)⁸
• 8(2x + 2)(x - 5)⁷ + 2(x - 5)⁸
• 2(x - 5)⁸
• 16(x - 5)⁷

Which rule would you need to use?

• Power Rule
• Product Rule
• Quotient Rule
• Chain Rule