Derivatives SET A

Find the derivative of f(x) = 3x^2 using the power rule.

• 9x

• 2x^3

• 6x

• 3x

Calculate the derivative of g(x) = 4sin(x) using the chain rule.

• 4tan(x)

• 4sin(x)

• 4cos(x)

• 4cos^2(x)

Find the derivative of k(x) = 2x^3 * cos(x) using the product rule.

• 2x^3 * sin(x) + 6x^2 * cos(x)

• 2x^3 * sin(x) - 6x^2 * cos(x)

• -2x^3 * sin(x) + 6x^2 * cos(x)

• -2x^3 * cos(x) + 6x^2 * sin(x)

Calculate the derivative of m(x) = 4x^2 / (3x + 2) using the quotient rule.

• m'(x) = (8x(3x + 2) - 4x^2(3x)) / (3x + 2)^2

• m'(x) = (8x(3x + 2) - 4x^2(2)) / (3x + 2)^2

• m'(x) = (8x(3x + 2) - 4x^2) / (3x + 2)^2

• m'(x) = (8x(3x + 2) - 4x^2(3)) / (3x + 2)^2

Determine the derivative of n(x) = ln(2x) using the logarithmic differentiation.

• n'(x) = (2/x)

• n'(x) = (x)

• n'(x) = (1)

• n'(x) = (1/x)

Find the derivative of p(x) = 3tan(x) using the chain rule and trigonometric functions.

• 3cot^2(x)

• 3cos^2(x)

• 3sec^2(x)

• 3sin^2(x)

Calculate the derivative of q(x) = 2arcsin(x) using the chain rule and inverse trigonometric functions.

• 2 / (1 - x^2)

• 2 / (x - 1)^2

• 2 / (1 + x^2)

• 2 / sqrt(1 - x^2)

Determine the derivative of r(x) = 4e^x * cos(x) using the product rule and exponential functions.

• -4e^x * sin(x) - 4e^x * cos(x)

• 4e^x * sin(x) + 4e^x * cos(x) + 4e^x

• -4e^x * sin(x) + 4e^x * cos(x)

• 4e^x * sin(x) - 4e^x * cos(x)

Find the derivative of s(x) = 3x^2 * ln(x) using the product rule and logarithmic functions.

• s'(x) = 3x^2 * (1/x) + 3x * ln(x)

• s'(x) = 3x^2 * (1/x) + 3x^2 * ln(x)

• s'(x) = 3x^2 * (1/x) + 6x * ln(x)

• s'(x) = 3x^2 * (1/x) + 6 * ln(x)

Find the derivative of h(x) = 5x^3 * tan(x) using the product rule and trigonometric functions.

• 5x^3 * sec^2(x) + 15x^2 * tan(x)

• 5x^3 * sec^2(x) - 15x^2 * tan(x)

• -5x^3 * sec^2(x) + 15x^2 * tan(x)

• -5x^3 * sec^2(x) - 15x^2 * tan(x)