Calculus Skills Test

What is the derivative of f(x) = 3x^2?

• 2x

• 3x^2

• 9x

• 6x

• x^2

Find the derivative of g(x) = sin(x) + cos(x).

• g'(x) = sin(x) + sin(x)

• g'(x) = cos(x) - sin(x)

• g'(x) = sin(x) - cos(x)

• g'(x) = cos(x) + cos(x)

Calculate the derivative of h(x) = ln(x).

• 1/x^2

• x^2

• 1

• 1/x

• x

If f'(x) = 4x^3, what is the original function f(x)?

• f(x) = x^3 + C

• f(x) = 4x^2 + C

• f(x) = 2x^4 + C

• f(x) = x^4 + C

Determine the derivative of y = e^x.

• e^2x

• 2e^x

• x^e

• e^x

What is the derivative of the function f(x) = 1/x?

• 2/x

• x

• 1/x^2

• -1/x

• -1/x^2

Find the derivative of the function y = sqrt(x).

• dy/dx = 1/(2*sqrt(x))

• dy/dx = 1/(2x)

• dy/dx = sqrt(x)

• dy/dx = 2/(sqrt(x))

If g'(x) = 2cos(x), what is the original function g(x)?

• g(x) = 2cos(x) + C

• g(x) = 2sin(2x) + C

• g(x) = 2tan(x) + C

• g(x) = 2sin(x) + C

Calculate the derivative of the function y = tan(x).

• y' = sec^2(x)

• y' = cos(x)

• y' = csc^2(x)

• y' = cot(x)

What is the derivative of the function f(x) = e^(2x)?

• e^(2x)

• 2*e^(2x)

• 4*e^(2x)

• 2e^(2x)