Chain Rule Implicit Differentiation Inverse Functions

Find dy/dx at a given point.

• 5/4

• 4/5

• 1

• -5

• -3
• 8
• 0
• 9

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• 
• 
• 

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

Which rule would you need to use?

• Power Rule

• Product Rule

• Quotient Rule

• Chain Rule

Use implicit differentiation to find y' for the following equation:   4x cos(y) = 1

• y' = cos(y) / x sin(y)

• y' = 4x sin(y)

• y' = cot(y)

• y' = 4 / sec(y)tan(y)

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) = (x² +1)⁶

• 12(x² + 1)⁶

• 12x(x² + 1)⁶

• 12x(x² + 1)⁵

• 12(x² + 1)⁵

Differentiate f(x) = (9 - 4x²)^-1

• 8x/(9 - 4x²)^-2

• 8x/(9 - 4x²)²

• -8x/(9 - 4x²)^-2

• -8x(9 - 4x²)²

If f(x)=(6x²-5x)⁷
what is f'(x)?

• 7(6x²-5x)⁶

• 7(6x²-5x)⁶⋅(12x)

• 7(6x²-5x)⁶⋅(12x-5)

• (12x-5)