Chain rule practice

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)

Find the derivative. 
g(x) = sin(cos²4x)

• -8cos(cos²4x)sin4xcos4x
• -8cos(cos²4x)sin4x
• -4cos(cos²4x)sin4x
• 8cos(cos²4x)sin4xcos4x

Find y' if y = tan(3x²+2).

• sec²(3x²+2)
• 6xsec²(3x²+2)
• 6xsec²x(3x²+2)
• sec²(6x)

Use the chart to find f'(3) for f(x) = g(x)/[2h(x)]

• (2π+3)/9
• -(3+2π)/9
• -(6+4π)/9
• -2(3+4π)/9

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)
• f '(x) = 30x⁶(x⁶ + 4)

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 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

Find the derivative of y = √(x² - 7)

• x/√(x² - 7)
• (x - 7)/√(x² - 7)
• (x² - 7)^(3/2)
• 1/√(x² - 7)

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