Differential Calculus is one of the most important topics in the preparation of IIT JEE. This is the easiest part of Calculus and there is no doubt in the fact that it is scoring too. It is also important to attain proficiency in Differential Calculus as it is a prerequisite to the learning of Integral Calculus too. Differential Calculus is a branch of mathematical analysis which deals with the problem of finding the rate of change of a function with respect to the variable on which it depends. So, differential calculus is basically concerned with the calculation of derivatives for using them in problems involving nonconstant rates of change. Applications also include computation of maximum and minimum values of a function. The study of Differential Calculus includes Functions, Sets, and Relations though they are considered to be a part of Algebra. Limits, Continuity, and Differentiability are the favorite topics of those who have a bent towards Differential Calculus. It is not only an easy topic but also fetches a direct question in the examination. A person who has already done a good practice of this chapter is also likely to do well in the next topic of Differentiation. The lifeline of Differential Calculus is basically the topics that include the application of Derivatives i.e.Tangent and Normal and Maxima and Minima. Differential calculus is closely related to integral calculus. In fact, differentiation is the reverse process of integration. This includes: 1. Set, Relations, and Functions 2. Limits, continuity, and Differentiability 3. Differentiation 4. Application of derivatives

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The inverse trigonometric functions sin−1(x) , cos−1(x) , and tan−1(x) , are used to find the unknown measure of an angle of a right triangle when two side lengths are known.

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A function f has limit L as x→a if and only if f has a left-hand limit at x=a, has a right-hand limit at x=a, and the left- and right-hand limits are equal. ... A function f is differentiable at x=a whenever f′(a) exists, which means that f has a tangent line at (a,f(a)) and thus f is locally linear at the value x=a.

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Differentiation allows us to find rates of change. ... If y = some function of x (in other words if y is equal to an expression containing numbers and x's), then the derivative of y (with respect to x) is written dy/dx

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The derivative is defined as something which is based on some other thing. In Mathematics, Derivative is an expression that gives the rate of change of a function with respect to an independent variable.

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