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Understanding the Power Rule for Derivatives in Calculus

Dec 31, 2025

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In this video, we explore the Power Rule, a fundamental principle for finding derivatives in calculus. The Power Rule states that if you have a function of the form f(x) = x^n, where n is a real number, the derivative f'(x) can be found using the formula f'(x) = n * x^(n-1). This rule simplifies the differentiation process, making it easier to work with polynomial functions. Join us as we discuss examples and applications of the Power Rule to strengthen your understanding of calculus concepts.

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Understanding the Power Rule for Derivatives in Calculus

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Presentation Transcript

The Power Rule for Derivatives http://www.youtube.com/watch?v=fUVf-qKaGzo 0-2:00, 6:00-6:20

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B1.1 &amp; B2.1 – Derivatives of Power Functions - Power Rule, Constant Rule, Sum and Difference Rule . IBHL/SL Y2 - Santowski. (A) Review. The equation used to find a tangent line or an instantaneous rate of change is: which we also then called a derivative. So derivatives are calculated as .

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Anti Power Rule

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4.1 The Product Rule and Power Rules for Exponents

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2.3 The product rule, quotient rule, and higher order derivatives

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2.3 The product rule, quotient rule, and higher order derivatives

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§2.3 The Chain Rule and Higher Order Derivatives

§2.3 The Chain Rule and Higher Order Derivatives. The student will learn about. composite functions,. the chain rule, and. nondifferentiable functions. Composite Functions. Definition. A function m is a composite of functions f and g if

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2 nd Derivatives, and the Chain Rule (2/2/06)

2 nd Derivatives, and the Chain Rule (2/2/06). The second derivative f '' of a function f measures the rate of change of the rate of change of f .

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Derivatives Product Rule

By Nathan Mehta Period 4 MACH 5. Derivatives Product Rule. Find the Derivative of f(x)=X 4 [5X-1] 3. f(x)=X 4 [5X-1] 3 Original Equation f ’(x)=4X 3 [5X-1] 3 + X 4 ( 3)(5X-1) 2 (5) Get the derivative of X 4 by using the Power Rule and leave [5X-1] 3 as is

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Power Rule

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Derivative – Power Rule, Product Rule, Chain Rule, Quotient Rule

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Power Rule for 100

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Derivatives Chain Rule

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Power Rule

Power Rule. k(x) = g n (x) = [g(x)] n k’(x) = n [g (x)] n-1 g’(x). Power Rule. k(x) = g n (x) = [g(x)] n k’(x) = n [g (x)] n-1 g’(x). k(x) = (x 2 - 4) 4 k’(x)=. 4 (x 2 - 4) 3 (2x) 4 (2x) 3 4 (x 2 - 4) 3 (2x - 4). t(x) = t’(x)=.

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Computations of the Derivative: The Power Rule

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4.1 The Power Rule

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Power Rule is a corallary to Chain Rule

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Understanding the Power Rule for Derivatives in Calculus

Understanding the Power Rule for Derivatives in Calculus

Presentation Transcript

B1.1 &amp;amp; B2.1 – Derivatives of Power Functions - Power Rule, Constant Rule, Sum and Difference Rule

Anti Power Rule

4.1 The Product Rule and Power Rules for Exponents

2.3 The product rule, quotient rule, and higher order derivatives

2.3 The product rule, quotient rule, and higher order derivatives

§2.3 The Chain Rule and Higher Order Derivatives

2 nd Derivatives, and the Chain Rule (2/2/06)

Derivatives Product Rule

Power Rule

Derivative – Power Rule, Product Rule, Chain Rule, Quotient Rule

Power Rule for 100

The Power Rule Review and The Product Rule

Calculus 2413 Chapter 3(3) Product Rule Quotient Rule Higher Derivatives

Derivatives Chain Rule

Power Rule

Section 6.1 Polynomial Derivatives, Product Rule, Quotient Rule

The Power Rule

Computations of the Derivative: The Power Rule

The Power Rule

Logarithm Properties - Power Rule

4.1 The Power Rule

Power Rule is a corallary to Chain Rule

B1.1 & B2.1 – Derivatives of Power Functions - Power Rule, Constant Rule, Sum and Difference Rule