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Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure $ P $ of the gas is inversely proportional to the volume $ V $ of the gas.(a) Suppose that the pressure of a sample of air that occupies $ 0.106 m^3 at 25^{\circ} C $ is 50 kPa. Write $ V $ as a function of $ P. $(b) Calculate $ dV\mid dP $ when $ P $ = 50 kPA. What is the meaning of the derivative? What are its units?

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02:31

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Oregon State University

University of Nottingham

Idaho State University

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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Boyle's Law states th…

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Boyle's Law The press…

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Boyle's law Boyle…

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Boyle's law for enclo…

it's clear. So when you married here. So we have PV equals K. He has a constant. We're gonna substitute 50 for P and 500.106 for ve me get Kate is equal to 5.3 and B is equal to 5.3 Overpay for part B V is equal to 5.3. Overpay p is equal to 50 Killer Paschal's. We're going to find the derivative of RV. This becomes equal to negative 5.3 he the negative to power. This could be rewritten as negative 5.3 over a piece square. Then we plug in 50 when we got negative 0.212 meters cubed over Killa Pasko's. And this represents the rate of change of the volume in respect to the pressure.

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