# RD Sharma Class 12 Chapter 11 Solutions (Differentiation)

RD Sharma Class 12 Maths Solutions for Chapter 11 ‘Differentiation’, are designed to help you find correct solutions to all the questions. The RD Sharma Solutions here are curated to help you fully prepare to ace your CBSE and advanced levels competitive examinations like JEE and NEET. These RD Sharma solutions play a major role in helping you acquire the concept and work on its application in different levels of mathematical problems you get.

RD Sharma Class 12 Maths Chapter 11 entails topics such as Introduction to Differentiation, Recapitulation, Differentiation of Inverse Trigonometric Functions From First Principles, theorem, Differentiation of a Function, Differentiation of Inverse Trigonometric Functions by Chain Rule, Differentiation by Using Trigonometric Substitutions, Relations between dy/dx and dx/dy, Differentiation of Implicit Functions, Logarithmic Differentiation, Differentiation of Infinite Series, Differentiation of Parametric Functions, Differentiation of a Function w.r.t another Function, and Differentiation of Determinants.

The Solutions provided in RD Sharma Class 12 Maths Chapter 11 comprise problems and their respective solutions in detail. With a total of 8 Exercises and 128 questions in detail in the easiest possible language and method, you’ll gain the most basic knowledge of what Differentiation is all about. With more than a hundred questions, all related to Differentiation, you’ll prepare well for CBSE, JEE Main and JEE Advanced.

Practising RD Sharma Class 12 Solutions for Maths Chapter 11 will make you understand the in-depth concept of the topic of Differentiation. The easy to understand the language of these solutions by Instasolv has helped thousands of students solve the most advanced problems in Differentiation.

## Important Topics for RD Sharma Class 12 Maths Solutions Chapter 11 Differentiation

**Introduction to differentiation**

If we find a function differentiable at all points in a given domain, then we can associate each point in that domain to the function’s derivative at that point. This correspondence among the points in the given domain and values of derivatives at those specific points results in a new function we call a differentiation of that function or derivative of that function. You may also call function f’s differentiation or derivative w.r.t x as f(x)’s differential coefficient.

**Differentiation of a Function of a Function**

**Theorem – Chain Rule –**

F(x) and g(x) are the two differentiable functions, then fog will always be differentiable.

(Fog)’(x) = f’(g(x))g’(x)

Or d/dx {(fog)(x)} = d/dg(x){(fog)(x)}d/dx (g(x))

**Differentiation of Inverse Trigonometric Functions by Chain Rule**

**Theorem 1. Chain Rule**

If x∈ (-1, 1), then you’ll find the differentiation of sin -1 x w.r.t x will always be 1/ (square root of (1-x²))

**Theorem 2. **If x∈ (-1, 1), then you’ll find the differentiation of cos -1 x w.r.t x will always be -1/ (square root of (1-x²))

**Theorem 3. **You’ll find the differentiation of tan -1 x w.r.t x will always be 1/ (1+x²)

**Theorem 4. **You’ll find the differentiation of cot -1 x w.r.t x will always be 1/ (1+x²)

**Theorem 5 **If x∈ R -[-1,1], then you will always find the differentiation of sec -1 x w.r.t x is 1/ |x| (square root of (x²-1))

**Theorem 6 **If x∈R -[-1,1], then you find the differentiation of cosec -1 x w.r.t x will be -1/ |x| (square root of (x²-1))

**Differentiation by using Trigonometric Substitutions**

- sin 2A = 2 Sin A cos A
- (1+cos2A) = 2cos²A
- 1- cos 2A = 2sin²A
- sin 2A = 2 tan A/(1+tan² A)
- cos 2A = (1-tan² A)/(1+tan² A)
- tan 2A = 2tanA/(1-tan² A)
- sin 3A = 3 sin A – 4 sin³A
- cos 3A = 4 cos³A – 3 cos A
- tan 3A = (3 tan A – tan³ A)/(1-3tan²A)

## Discussion of Exercises for RD Sharma Class 12 Maths Solutions for Chapter 11

- Exercise 11.1 helps you to find the derivative of a function using the first principle method
**Exercise 11.2 talks about differentiating the given functions w.r.t x**- Exercise 11.3 teaches you about differentiating the functions w.r.t x
- With Exercise 11.4, you’ll learn more about finding the value of dy/dx
- Exercise 11.5 is similar to the first three exercises only with advanced level problems of finding the differentiation of a given function w.r.t x
- Exercise 11.6 reflects more on variables with higher values and proving their differentiation.
- Exercise 11.7 will ask you to find dy/dx given the value of two variables.
- Exercise 11.8 talks about differentiating a variable w.r.t another

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