Derivatives of actual functions

Lecture Calculus - Chapter 9: Computing derivatives. After studying this section will help you understand: we list and prove the rules first, they are rather easy to prove; let us state all five of them as one theorem, and prove it,...

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Partial nephrectomy (PN) preserves renal function and has become the standard approach for T1a renal cell carcinoma (RCC). However, there is still an ongoing debate as to which patients will actually derive greater benefit from partial than from radical nephrectomy (RN).

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THE TERM CELL IS DERIVED from the Latin cella, meaning storeroom or chamber. It was first used in biology in 1665 by the English botanist Robert Hooke to describe the individual units of the honeycomb-like structure he observed in cork under a compound microscope. The “cells” Hooke observed were actually the empty lumens of dead cells surrounded by cell walls, but the term is an apt one because cells are the basic building blocks that define plant structure.

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The rest of this paper is structured as follows. In section 2, we discuss previous literature that has addressed the questions in which we are interested. Section 3 shows basic demographic data for the United States. In section 4 we present and solve the theoretical model that we will be using. Section 5 applies the model to derive optimal paths of consumption and of asset prices in the face of demographic change. The section begins by considering an stylized case of population aging, which is used to develop intuition.

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There are times, however, when we are more interested in finding the function from which the integrand came (i.e., finding the antiderivative) than in finding the actual change. Then we must recognize that the derivative of a constant is zero, so any arbitrary constant added to the integral vanishes in finding the integrand. Thus we may write ∫ − nRT dP nRT = +c 2 P P (A34) where c is an arbitrary, or unknown, constant. Such an expression is called an indefinite integral. 7/10/07 A- 131 ...

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