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Differentiation is the chief chapter in Differential Calculus. It is these concepts which form the basis of entire Calculus. This further helps in the subsequent chapter of Tangents and Normal and Maxima Minima.
Normally a dependent variable is expressed in terms of independent variables by means of an equation. Now when we find the differential coefficient of the dependent variable with respect to the independent variable, what we are doing is to try to find out another equation by which the change in the dependent variable (for any infinitesimal change in independent variable) is relatable to the independent variable, whatever be the value of the independent variable.
"Differentiation" is one of the easiest and important chapters of Calculus in the Mathematics syllabus of IIT JEE, AIEEE and other engineering examinations. In this section we'll discuss in detail the geometrical significance of differential co-efficient and various ways to carry out the differentiation of different functions. These laws are not only important from the point of view of Mathematics but they are also very useful to a large extent in Physics and Physical Chemistry. The examples based on this are very easy and can be helpful in mastering the topic.
The chapter is important not only because it fetches 3-4 questions in most of the engineering examination but also because it is prerequisite to the subsequent chapters of Differential Calculus.
Differentiation is important from the perspective of scoring high in IIT JEE as there are few fixed pattern on which a number Multiple Choice Questions are framed on this topic. You are expected to do all the questions based on this to remain competitive in IIT JEE examination. It is very important to master these concepts at early stage as this forms the basis of your preparation for IIT JEE, AIEEE, DCE,EAMCET and other engineering entrance examinations.