Differentiation is a term in calculus, which is one of the two important concepts in mathematics apart from integration. It is also considered a method of finding the derivative of a function. Differentiation is a mathematical process where we find the instantaneous rate of change in function based on one of its variables. A common example is the rate of change of displacement with respect to time which is called velocity. Anti-differentiation is nothing but the opposite of finding a derivative or, in other words, integration.
In RD Sharma Solutions for Class 12th Maths Chapter 11, students also study the recapitulation of the product rule, quotient rule and differentiation of a constant with an illustration. Moreover, other important topics are also being covered in this chapter. One such concept is the differentiation of inverse trigonometric functions using the first principle.
Additionally, they also learn what a chain rule is, define them, and use them precisely in problems. In case if we want to differentiate a function of a function, y=f g x, i.e. to find dy/dx, we need to do two things. One is substitute u=g (x). This gives, y=f (u). Next is to use a formula called chain rule.
The chain rule can also be used to differentiate inverse trigonometric functions by using the chain rule. Furthermore, concepts, namely differentiation using trigonometric substitutions and differentiation of implicit functions, are also taught to students.
Logarithmic differentiation is another important topic that is being covered in this chapter. Other than this, some key topics such as differentiation of infinite series, differentiation of parametric functions and differentiation of denominators are also taught. Lastly, they also get exposed to know how to differentiate a function with respect to another function.