Derivatives of Polynomials

Find the derivative of the given equation
f(x) = x⁴ + 4x³ - 2x²

• x³ + x² - x

• 4x³ + 12x² + 4x

• 4x + 12x - 4x

• 4x³ + 12x² - 4x

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Find \frac{dy}{dx}, If \ y= \frac{x^3}{3}+ \frac{x^2}{2}+x .

Find the derivative
f(t) = (t² + 2t)⁵

• f'(t) = 5(2t+2)⁴

• f'(t) = 5(t² + 2t)⁴

•  f'(t) = 5(t² + 2t)⁴(2t)

• f'(t) = 5(t² + 2t)⁴(2t + 2)

Find the derivative of y = 2x² (3x - 4)

• 6x³ - 8x²

• 18x² - 16x

• 15x² - 6x

• 6x - 4

Differentiate h(x) = 3x^5/3 - 6x^1/6 + 3x

• h'(x) = 5x^2/3 - x^-5/6 + 3

• h'(x) = 3x^2/3 - 6x + 3

• h'(x) = 5x^4/3 - 6x + 3

• h'(x) = 3x^4/3 - x^-5/6 + 3

This rule is used to differentiate functions of the form f(x) = x^r, whenever r is a real number.

• The Sum, Difference, and Constant Multiple Rules

• The Product Rule

• The Quotient Rule

• The Power Rule

This rule says that the derivative of a product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function.

• The Product Rule

• Constant Multiple Rule

• The Power Rule

• The Constant Rule

To find derivatives of polynomials and rational functions efficiently without resorting to the limit definition of the derivative, we must first develop _____ for differentiating these basic functions.

Identify whether the following is differentiable and continuous: y=5x-1, x = 1

• continuous

• differentiable

• continuous and differentiable

• not continuous nor differentiable