RD Sharma Class 12 Solutions Chapter 11 - Differentiation (Ex 11.5) Exercise 11.5

The chapter

‘Differentiation’ is Chapter 11 of RD Sharma Class 12 Maths to help the students to learn about differentiation and how to find derivatives of simple functions. The two important parts of calculus are differentiation and calculus. The process of finding the derivative, or rate of change, of a function, is known as Differentiation. Differentiation is the process that can be carried out by purely algebraic manipulations, using three basic derivatives and four rules of operations.

Differentiation can be applied to measure the function per unit change in the independent variable. An example of differentiation is that the speed is calculated as the rate of change of distance concerning time a very basic derivatives (D) are- 

1. for algebraic functions, D (xⁿ)= nx^n-1, in which n is any real number; 

2. for trigonometric functions, D(sin x)= cos x; and 

3. for exponential functions, D(e^x)= e^x

Formulas Used in Differentiation 

Basic Differentiation Formulas

Let us consider f(x) is a function and f’x is a derivative of the function

Rules for Differentiation

There are 4 rules of Differentiation-

1. Sum and Difference Rule

The derivative of a sum is equal to the sum of the derivatives

\[\frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]\]

The derivative of a difference is equal to the difference of the derivatives

\[\frac{d}{dx}[f(x) - g(x)] = \frac{d}{dx}[f(x)] - \frac{d}{dx}[g(x)]\]

2. Product Rule

If f(x).g(x) is a function, then the derivative of the function is

\[\frac{d}{dx}[f(x).g(x)] = {f}'x.g(x) + f(x).{g}'(x)\]

3. Quotient Rule

If f(x)=u(x)/v(x) is a function, then the derivative of the function is 

\[{f}'x={[\frac{u(x)}{v(x)}]}'=\frac{v(x)\times {u}'(x)-u(x)\times {v}'(x)}{[v(x)]^{2}}\]

4. Chain Rule

If y=f(x)=g(u) and if u=h(x), then the chain rule for differentiation will be

\[\frac{dy}{dx}=\frac{dy}{du}\times \frac{du}{dx}\]

Advantages of RD Sharma Maths for Class 11

If the students are preparing for competitive exams they should definitely go for RD Sharma Maths for Class 11. RD Sharma Maths Class 11 provides a clearer understanding of each and every topic. Since the main goal is to maintain quality while studying, not quantity there it is best to refer to RD Sharma books in which all topics are explained in detail and systematic way.

There are Many Other Advantages of RD Sharma Maths for Class 11 such as-

• One of the main advantages of RD Sharma is that there are various types of questions available. It has basic level questions for mediocre students as well as for the students who want to test their critical thinking, they have Higher Order Thinking Skill questions.

• Another advantage is that all the questions are divided into different sub-types so that the students are aware of all the types of questions that can be formed out of one question and can be asked in an exam

• All the topics are explained in detail which gives the student a clear picture of the concept and helps them to study the concept to its core.