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A particle moves along the curve $ y = 2 \sin (\pi x/2). $ As the particle passes through the point $ (\frac {1}{3}, 1). $ its $ x- $ coordinate increases at a rate of $ \sqrt {10} cm/s. $ How fast is the distance from the particle to the origin changing at this instant?

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Distance of the particle from origin is increasing at the rate of 9.2 $\mathrm{cm} / \mathrm{s}$

03:16

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

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.

07:16

A particle moves along the…

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04:16

A particle is moving along…

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Particle Motion A particle…

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we know, given the fact that wise to sign of plaques over to we know he can write d y over DT as hi co sign Pi over six times word of 10 which simplifies to be pie squared of 30 over too. Which tells us then that d s over DT is gonna be one over too squared of 1/3 squared plus one squared times two times 1/3 snow. We're just putting in time squirt of 10 plus two times one times pi squirt of 30 over too, which we convince Simplify to D s over. DT is approximately 9.2 centimeters per seconds. The distance of the particle from the origin is increasing its positive 9.2 centimeters per second.

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