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Differential Calculus
Abstract
In this chapter, we deal with differential calculus. By definition of differentiation, its interpretations we will derive the differentiations of several functions which are defined in Chapter 3. Besides finding tangent and normal lines, some more applications of differentiation will be given throughout the chapter. Another interpretation of the derivative, which is the instantaneous speed that is observed in physics, will also be considered here and give some examples of its application. After introducing the concept of differential, we introduce chain rules and parametric differentiation. The concepts maxima and minima for functions will be described. We will state Roll's, Lagrange's and Cauchy's theorems as an optional part and then introduce Taylor's formula, which is the most useful one in calculus.
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