Chain Rule Differentiation

What rule should be used in deriving h(x) = 2(x - 4)³

• Power rule

• Product rule

• Quotient rule

• 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) = (x² +1)⁶

• 12(x² + 1)⁶
• 12x(x² + 1)⁶
• 12x(x² + 1)⁵
• 12(x² + 1)⁵

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

Differentiate f(x) = (9 - 4x²)^-1

• 8x/(9 - 4x²)^-2

• 8x/(9 - 4x²)²

• -8x/(9 - 4x²)^-2

• -8x(9 - 4x²)²

find y' for y= (2x+1)¹⁰

• 10(2x+1)⁹

• 20(2x-1)⁹

• 20(2x+1)¹⁰

• 20(2x+1)⁹

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)

Tags

CCSS.8.F.A.3

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

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Find the derivative of:
f(x) = 7(3x + 4)⁵

• 35(3x + 4)⁵
• 35(3x + 4)⁴
• 105(3x + 4)⁵
• 105(3x + 4)⁴