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If two resistors with resistances $ R_1 $ and $ R_2 $ are connected in parallel, as in the figure, then the total resistance $ R, $ measured in ohms $ (\Omega), $ is given by$ \frac {1}{R} = \frac {1}{R_1} + \frac {1}{R_2} $If $ R_1 $ and $ R_2 $ are increasing at rates of $ 0.3 \Omega/s $ and $ 0.2 \Omega/s, $ respectively, how fast is $ R $ changing when $ R_1 = 80 \Omega $ and $ R_2 = 100 \Omega? $

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03:06

Wen Zheng

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 9

Related Rates

Derivatives

Differentiation

Baylor University

University of Michigan - Ann Arbor

University of Nottingham

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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Okay. Recall the fact that we have our run R two d r one over d, t and D are two over DT in this problem. Therefore, we know we can write out an equation. One over R is one of 11 over 80 plus one over r two. This simplifies to nine over 400 if we hop eight common denominators simplified which gives us our is 400 over nine because of one over ours. Not over 400 men are over. One of just our is 400 over nine. Therefore, we know we can multiply 400 over nine squared comes one over 80 squared times 0.3 plus one over 100 squared times 0.2 and then we know we can simplify to get 0.132 on the November. This is in terms of the units for resistance

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