Derivatives with Chain Rule

Differentiating can help us find the . . .

• .... area under a curve

• ... rate of change at a particular value

• ... gradient of a function

• ... most optimal solution for a function

• ... perpendicular gradient of a straight line

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

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

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

Find the derivative of the given equation
f(x) = 7

• 7
• 0
• 7x
• 14