Chain Rule

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 (sin²x) = ?

• 2sin x
• 2(sin x)(cos x)
• 2cos x
• 2x(cos x)

Find dy/dx for
(3x - 2x²)³

• dy/dx = (3 - 4x)⋅3(3x - 2x²)²
• dy/dx = 3(3x - 2x²)²
• dy/dx = 3(3 - 4x)²
• dy/dx = (3 - 4x)(9x - 18x²)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)

Which rule would you need to use?

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

Which rule would you need to use?

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

.

• Only the Quotient Rule
• The Quotient and Product Rules
• The Quotient and Chain Rules
• Only the Chain Rule

Find an equation of the tangent line to the graph of f(x) at the point (1, 100)
f(x) = (5x⁵ + 5)²

• y = 500x + 400
• y = 100x + 400
• y = -500 x - 400
• y = 500x - 400

When do you use the chain rule?

• anytime you want
• when there is a function in a function
• where there are multiple layers to a lasagna (yum)
• when there is division

The derivative of a function is its

• Average Slope
• Maximum/Minimum
• Instantaneous rate of change
• Common Denominator