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Use the definition of a derivative to show that if $ f(x) = 1/x, $ then $ f'(x) = -1/x^2. $ (This proves the Power Rule for the case $ n = -1.$ )

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01:01

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Missouri State University

Baylor University

University of Nottingham

Boston College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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Power Rule for Functions S…

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If $f(x)=x,$ then $f^{\pri…

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Let $f(x)=x^{n}$ and $g(x)…

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Show that for any power fu…

04:43

Find a formula for the der…

01:32

Use the General Power Rul…

Hey, it's clear, So enumerated here. So we have up of access equal Thio one over X. Yeah, if the door If it is, it's equal to limit. As each approaches Ciro one over X Plus H minus one over X over each becomes equal to the limit knows each approaches Ciro for a negative H over X X plus H over each. This is equal to limit as each approaches. So for negative one over X terms X plus H, which is equal to negative one over X square.

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