Calculus Rules Practice

Differentiate the function y = x^2 * e^x using the product rule.

• y' = x^2 * e^x + e^x

• y' = x^2 + 2x * e^x

• y' = x^2 * e^x + x * e^x

• y' = x^2 * e^x + 2x * e^x

Find the derivative of y = (3x + 2) / (x - 1) using the quotient rule.

• -3 / (x - 1)^2

• -5 / (x - 1)^2

• -2 / (x - 1)^2

• 5 / (x - 1)^2

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

• 2cos(x)

• cos(2x)

• 2cos(2x)

• 4cos(2x)

• sin(2x)

Use the product rule to differentiate y = x^3 * cos(x).

• y' = 3x^2 * sin(x) + x^3 * cos(x)

• y' = 3x^2 * cos(x) + x^3 * sin(x)

• y' = 3x^2 * sin(x) - x^3 * cos(x)

• y' = 3x^2 * cos(x) - x^3 * sin(x)

Apply the quotient rule to find the derivative of y = (2x^2 + 1) / (x^2 - 1).

• (6x(x^2 - 1) + 2x(2x^2 + 1)) / (x^2 - 1)^2

• (6x(x^2 - 1) - 2x(2x^2 - 1)) / (x^2 - 1)^2

• (6x(x^2 + 1) - 2x(2x^2 - 1)) / (x^2 - 1)^2

• (6x(x^2 - 1) - 2x(2x^2 + 1)) / (x^2 - 1)^2

Find the derivative of y = e^(3x^2) using the chain rule.

• 6x * e^(3x^2)

• 3x * e^(3x^2)

• 9x * e^(3x^2)

• 6x^2 * e^(3x^2)

Differentiate the function y = x^4 * ln(x) using the product rule.

• 4x^3 * ln(x) + 3x^2

• 4x^3 * ln(x) - x^3

• 4x^3 * ln(x) - 3x^2

• 4x^3 * ln(x) + x^3

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

• 2x * sec^2(x^2)

• 2x * tan(x^2)

• x * sec^2(x^2)

• 4x * sec^2(x^2)

Use the product rule to find the derivative of y = x^2 * sin(x).

• 2x * sin(x) + x^2 * cos(x)

• 2x * cos(x) + x^2 * sin(x)

• 2x * sin(x) + x^2 * sin(x)

• 2x * sin(x) - x^2 * cos(x)

Apply the quotient rule to differentiate y = (3x - 1) / (2x + 1).

• (2(3x - 1) - (3)(2x + 1)) / (2x - 1)^2

• (2(3x - 1) + (3)(2x + 1)) / (2x + 1)^2

• (3(3x - 1) - (2)(2x + 1)) / (2x + 1)^2

• (2(3x - 1) - (3)(2x + 1)) / (2x + 1)^2