Derivatives of Polynomial Functions

Find the derivative of the function f(x) = 3x^4 using the power rule.

• f'(x) = 10x^3

• f'(x) = 16x^2

• f'(x) = 12x^3

• f'(x) = 9x^4

Calculate the derivative of g(x) = (2x^3)(5x^2) using the product rule.

• g'(x) = 6x^2 * 5x^2 - 2x^3 * 10x

• g'(x) = 12x^4 + 20x^4

• g'(x) = 10x^5 + 12x^4

• g'(x) = 6x^2 * 5x^2 + 2x^3 * 10x

Determine the derivative of h(x) = 4x^5 using the power rule.

• h'(x) = 20x^4

• h'(x) = 16x^4

• h'(x) = 25x^3

• h'(x) = 10x^5

Find the derivative of the function p(x) = (3x^2)(4x^3) using the product rule.

• 12x^5 + 24x^4

• 15x^5 + 30x^4

• 10x^5 + 20x^4

• 7x^5 + 18x^4

Calculate the derivative of q(x) = 2x^6 using the power rule.

• 12x^5

• 10x^4

• 8x^7

• 4x^3

Determine the derivative of the constant function m(x) = 7.

• 7

• 1

• 0

• Undefined

Determine the derivative of r(x) = (5x^4)(6x^3) using the product rule.

• 90x^6 + 30x^7

• 150x^11

• 10x^12

• 35x^7

Find the derivative of the function s(x) = 6x^7 using the power rule.

• 12x^6

• 42x^6

• 36x^7

• 18x^8

Calculate the derivative of t(x) = (3x^3)(2x^4) using the product rule.

• t'(x) = (3x^3)(2x^4) - (9x^2)(8x^3)

• t'(x) = (3x^3)(8x^3) + (9x^2)(2x^4)

• t'(x) = (3x^3)(8x^3) - (9x^2)(2x^4)

• t'(x) = (3x^3)(6x^4) + (9x^2)(2x^4)

Determine the derivative of u(x) = 7x^8 using the power rule.

• 56x^7

• 63x^9

• 14x^7

• 49x^8