Chain Rule Quiz

What is the chain rule used for in calculus?

• Multiplying two functions together

• Finding the derivative of a composite function

• Finding the integral of a composite function

• Dividing two functions

If f(x) = (3x² + 2x)⁴, find f'(x).

• 4(3x² + 2x)³(6x + 2)

• 4(3x² + 2x)³(3x + 2)

• 12x²(3x + 2)³

• 4(3x² + 2x)(6x + 2)

If g(x) = sin(2x), find g'(x) .

• g'(x) = 2sin(2x)

• g'(x) = sin(2x)

• g'(x) = 2cos(2x)

• g'(x) = cos(2x)

What is the derivative of cos(3x) ?

• -3cos(3x)

• -3sin(3x)

• 3cos(3x)

• 3sin(3x)

If h(x) = e^(4x), what is h'(x) ?

• 4e^(4x)

• 16e^(4x)

• 4e^(x)

• e^(4x)

Find the derivative of f(x) = cos(x)sin(2x)

• cos²x -sin²(2x)

• 2cos(x)cos(2x) +sin(2x)sin(x)

• 2cos(x)cos(2x)

  • - sin(2x)sin(x)

• 2cos(x)cos(2x)

  - 2sin(2x)sin(x)

If y = (2x + 3)⁵, what is dy/dx using the chain rule?

• 10(2x + 3)⁴

• 5(2x + 3)⁴

• 25(2x + 3)³

• 10(2x + 3)⁶

What is the chain rule formula for composite functions?

• u * v

• u'(v) * v'

• u' + v'