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Suppose $x=D(p)$ is a nonlinear demand equation. Let price change from $p$ to $p+h .$ Show that clasticity of demand is the limit as $h$ approaches zero of the relative change in demand to the relative change in price.

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 5

Applications II - Business and Economic Optimization Problems

Derivatives

Campbell 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.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

01:05

For the demand equation, f…

01:08

For the demand equations f…

07:57

Demand Solve the demand fu…

01:07

08:48

Find the demand function i…

02:43

Suppose that a demand func…

02:47

01:23

Explain why, if demand is …

So for the given problem, we're going to be doing implicit differentiation. We want to find the rate of change of P. With respect to act by differentiating implicitly. So if we have X equals P squared minus to E. Plus 1000, we end up seeing here is that we'll have one. When we differentiate that will get one equals two. P. Keep crime or bpd x minus two. Keep crime us uh zero. So we get rid of it. Then we can factor out the P. Prime. So we end up getting this right here, times P. Prime. Then we'll divide both sides by it. So keep private, going to equal this right here. So that's gonna be our final answer.

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