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The number of tree species $ S $ in a given area $ A $ in the Pasoh Forest Reserve in Malaysia has been modeled by the power function

$ S(A) = 0.882A^0.842 $

where A is measured in square meters. Find $ S' (100) $ and interpret your answer.

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01:47

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Campbell University

Harvey Mudd College

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.

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Hey, it's Claire. So when you read here, you have us of A is equal to 0.882 A. To the point 84 to power. We're going to differentiate it. Using the power of all we got a 0.743 A. It is a negative 0.158 power. We substitute 100 for a We get around 0.36 maybe around two decimals. And that means there are 100 tree species in 0.36 square meters.

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