Table of Derivatives and Integrals

Table of Derivatives and Integrals PDF - Overview

Table of Derivatives and Integrals contains information about the derivatives and Integrals in table format, In the Table of Derivatives, a and b are constants, independent of x, and in the  Table of Integrals a and b are given constants, independent of x and C is an arbitrary constant. It also tells about the Properties of Exponentials and the Properties of Logarithms.

Properties of Exponentials – In the following, x and y are arbitrary real numbers, a and b are arbitrary constants that are strictly bigger than zero and e is 2.7182818284, to ten decimal places.

Properties of Logarithms – In the following, x and y are arbitrary real numbers that are strictly bigger than 0, a is an arbitrary constant that is strictly bigger than one and e is 2.7182818284, to ten decimal places.

Table of Derivatives and Integrals

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Table of Derivatives and Integrals – Derivatives – The derivative of a function can be geometrically interpreted as the slope of the curve of the mathematical function f(x) plotted as a function of x. But its implications for the modeling of nature go far deeper than this simple geometric application might imply. After all, you can see yourself drawing finite triangles to discover slope, so why is the derivative so important? Its importance lies in the fact that many physical entities such as velocity, acceleration, force and so on are defined as instantaneous rates of change of some other quantity. The derivative can give you a precise intantaneous value for that rate of change and lead to precise modeling of the desired quantity.

Table of Derivatives and Integrals – Integrals – The integral of a function can be geometrically interpreted as the area under the curve of the mathematical function f(x) plotted as a function of x. You can see yourself drawing a large number of blocks to appproximate the area under a complex curve, getting a better answer if you use more blocks. The integral gives you a mathematical way of drawing an infinite number of blocks and getting a precise analytical expression for the area. That’s very important for geometry – and profoundly important for the physical sciences where the definitions of many physical entities can be cast in a mathematical form like the area under a curve.

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