Mastering Derivatives

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

• 2x

• x

• 2x^2

• x^3

Find the derivative of f(x) = 3x^3 - 5x + 2.

• 6x^2 - 5

• 9x^2 + 2

• 9x^2 - 5

• 3x^2 - 5

Using the product rule, find the derivative of f(x) = x^2 * sin(x).

• f'(x) = 2x cos(x) + x^2 sin(x)

• f'(x) = 2x sin(x) + x^2 cos(x)

• f'(x) = x^2 sin(x) + 2x cos(x)

• f'(x) = 2x^2 cos(x) + sin(x)

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

• e^x

• ln(x)

• x^e

• e^2x

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

• 1/x

• x

• ln(x) + 1

• 1

Using the quotient rule, find the derivative of f(x) = (x^2 + 1)/(x - 1).

• (2x)/(x - 1)

• (x^2 - 2x - 1)/(x - 1)^2

• (x^2 + 2x + 1)/(x - 1)^2

• (x^2 - 1)/(x + 1)^2

What is the derivative of f(x) = 5x^4?

• 10x^4

• 15x^2

• 25x^5

• 20x^3

Find the derivative of f(x) = cos(x).

• sin(x)

• -cos(x)

• tan(x)

• -sin(x)

Using the product rule, find the derivative of f(x) = (2x)(3x^2 + 1).

• 9x^2 + 1

• 12x^2 + 3

• 6x^2 + 2

• 18x^2 + 2

What is the derivative of f(x) = tan(x)?

• sec(x)

• sin(x)

• cos(x)

• sec^2(x)