Mastering Derivatives in Calculus

Calculate the derivative of f(x) = 3x^4 - 5x^2 + 2.

• 3x^3 - 5x^2 + 2

• 12x^2 - 10

• 12x^3 - 10x

• 6x^3 - 5x

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

• 10x^4 + 6x^2

• 4x^3 + 2x^2

• 6x^5 + 2x

• 8x^4 + 4x^2

Apply the quotient rule to find the derivative of f(x) = (x^2 + 1)/(x - 3).

• (x^2 - 6x - 1)/(x - 3)^2

• (x^2 + 6x + 1)/(x - 3)^2

• (2x)/(x - 3)

• (x^2 - 1)/(x + 3)^2

Use the chain rule to differentiate f(x) = sin(3x^2 + 2).

• f'(x) = 6x * cos(3x^2 + 2)

• f'(x) = 6 * cos(3x^2 + 2)

• f'(x) = 3x * cos(3x^2 + 2)

• f'(x) = 9x^2 * sin(3x^2 + 2)

Find the second derivative of f(x) = x^5 - 4x + 7.

• 12x^2 - 4

• 15x^4

• 5x^6

• 20x^3

Calculate the derivative of f(x) = e^(2x) * ln(x).

• f'(x) = e^(2x) * (2ln(x) + 1/x)

• f'(x) = e^(2x) * (ln(x) + 2)

• f'(x) = e^(2x) * (2/x)

• f'(x) = 2e^(2x) * ln(x)

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

• 4x^4 + 6x^2 - 2x

• 5x^4 + 6x^2 - 4x

• 5x^4 + 9x^2 - 4x

• 3x^4 + 9x^2 - 6

Apply the quotient rule to find the derivative of f(x) = (5x^2 + 1)/(2x - 4).

• (5x^2 - 8)/(2x - 4)

• (10x^2 + 40x + 2)/(2x - 4)^2

• (10x^2 + 2)/(2x - 4)^2

• (10x^2 - 40x - 2)/(2x - 4)^2

Use the chain rule to differentiate f(x) = (2x + 1)^4.

• 8(2x + 1)^3

• (2x + 1)^4

• 16(2x + 1)^2

• 4(2x + 1)^3

Find the third derivative of f(x) = 4x^3 - 6x^2 + 2x.

• 12

• 24

• 18

• 30