Differential Functions - Chain Rule

Find the derivative of y = sin(3x) using the chain rule.

• 3cos(3x)

• 3sin(3x)

• cos(3x)

• 3cos(x)

Calculate the derivative of y = e^(2x^2) using the chain rule.

• dy/dx = 4x^2 * e^(2x^2)

• dy/dx = 4x * e^(2x^2) * 4x = 8x^2 * e^(2x^2)

• dy/dx = 2x * e^(2x^2)

• dy/dx = 16x^3 * e^(2x^2)

Determine the derivative of y = ln(4x) using the chain rule.

• 4/x

• 1/4x

• 1/x

• x

• 4

Find the derivative of y = sqrt(5x + 3) using the chain rule.

• sqrt(5x + 3) / 5

• 5 / (2 * sqrt(5x + 3))

• 5 / (2 * (5x + 3))

• 2 / (5 * sqrt(5x + 3))

Calculate the derivative of y = cos(2x^3) using the chain rule.

• -6x^2sin(2x^3)

• -6x^2cos(x^6)

• -6x^2cos(2x^3)

• -6x^2sin(x^6)

Determine the derivative of y = tan(4x) using the chain rule.

• y' = 4sec(4x)

• y' = 4tan(4x)

• y' = 4cos(4x)

• y' = 4sec^2(4x)

Find the derivative of y = e^(sin(x)) using the chain rule.

• e^(cos(x)) * cos(x)

• e^(sin(x)) * sin(x)

• e^(cos(x)) * sin(x)

• e^(sin(x)) * cos(x)

Calculate the derivative of y = ln(cos(x)) using the chain rule.

• -tan(x)

• sec(x)

• cot(x)

• -sin(x)