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If a current $ I $ passes through a resistor with resistance $ R, $ Ohm's Law states that the voltage drop is $ V = RI. $ If $ V $ is constant and $ R $ is measured with a certain error, use differentials to show that the relative error in calculating $ I $ is approximately the same (in magnitude) as the relative error in $ R. $

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Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

Derivatives

Differentiation

Missouri State University

Baylor University

University of Michigan - Ann Arbor

Idaho State University

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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If a current $I$ passes th…

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$$ \begin{array}{l}{\text …

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Ohm's Law A current o…

Okay, The first thing, the nose, the eyes that could lead to the over our Therefore the derivative of I is negative v over R square. Do you are the relative error is changing? I over I In other words, d ie the derivative over I This is negative v over r squared d r over v over r, which is negative d r over our

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