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Differential calculus can be considered as mathematics of motion, growth and change where there is a motion, growth, change. Whenever there is variable forces producing acceleration, differential calculus is the right mathematics to apply..

Differentiation of certain functions seem to be very difficult, but by suitably substituting the independent variable with some trigonometric function or other functions, they can be differentiated easily. If f(x) involves inverse trigonometric functions of algebraic functions..

Introduction - Let us began this chapter with the following statement: Often a physician may want to test how small changes in dosage can affect the body's response to a particular drug. An economist may want to study how investment changes with variation in interest rates. How the velocity of a he..

Application of Derivatives Animation..

Let f be continuous on [a, b] and differentiable on the open interval (a, b). Then (a) f is increasing on [a, b] if f '(x) > 0 for each x (a, b) (b) f is decreasing on [a, b] if f '(x) < 0 for each x (a, b) This theorem can be proved by using Mean Value Theorem. We shall prove the theore..

Differentiation by Substitution - Differentiation of certain functions seem to be very difficult, but by suitably substituting the independent variable with some trigonometric function or other functions, they can be differentiated easily.Differentiation of certain functions seem to be very difficu..

In this chapter, we have studied various types of functions and their graphs. The use of graphs also facilitate the study of domain and range of functions.In this chapter, we have studied various types of functions and their graphs. The use of graphs also facilitate the study of domain and range of..

In algebra we come across certain products very frequently. For e.g., (a + b) 2 , (a + b) 3 (a + b + c) 2 etc. These are nothing but products of binomials or trinomials. We derive the formulae for these products and apply them whenever necessary. These expansions help us to ..

). Its usefulness is seen through emphasis on mathematising practical situations.Solving of problems depends on the ability to understand and apply mathematical analysis to different situations. In this chapter, we will study some fundamental definitions and application..

Rene' Descartes' (1596-1665), a French philosopher and mathematician, introduced a method by which the position of a point can be corresponded with an ordered pair of real numbers. These pair of real numbers are called the Coordinates. This method is the new idea of combining two branches of mathe..