# RS Aggarwal Class 12 Chapter 10 Solutions (Differentiation)

RS Aggarwal Solutions for Class 12 Chapter 10 Differentiation are prepared to help in learning the methods to solve the exercise questions. In the RS Aggarwal Solutions of this chapter, you will learn the fundamentals of Differentiation of certain kinds of functions, advancing a step ahead in Calculus. The functions that are covered in the exercises are mostly logarithmic, exponential and inverse trigonometric functions. Major topics covered in this chapter will help you excel in your higher studies as well. Thus, for a robust base, you must solve these questions besides relying on your school textbook.

There are a sum total of 143 questions in 10 exercises in this chapter. This will help you practise differentiation thoroughly as it is also a very scoring topic in the competitive exams. All the important functions in CBSE syllabus are also covered in detail in these questions. Adding this reference source in your study routine will help you in quick revisions besides absolute clarity in the concepts. You can also rely on the exercise solutions for completing your homework which will fill the gaps that would have been left in the classroom studies.

We, at Instasolv, take care of the most frequently occurring doubts among students. That is why you will find the RS Aggarwal Class 12 Solutions Chapter 10 Differentiation in line with your level of understanding as you will progress towards the more difficult questions. This will help you score better than your competitors and hence improve your rank significantly. At Instasolv, the questions are solved in a step by step fashion with detailed reasoning as expected by the Board.

## Topics Covered in RS Aggarwal Solutions for Class 12 Chapter 10 – Differentiation

**Differentiation of Inverse Trigonometric Functions:**

- Differentiation of sin
^{-1}x with respect to x is

Where x ϵ (-1, 1)

- Differentiation of cos
^{-1}y with respect to y is

Where x ϵ (-1, 1)

- Differentiation of tan
^{-1}x with respect to x is

Where x ϵ R

- Differentiation of cot
^{-1}x with respect to x is

Where x ϵ R

- Differentiation of sec
^{-1}y with respect to y is

Where x ϵ R – [-1, 1]

- Differentiation of cosec-1 x with respect to x is

Where x ϵ R – [-1, 1]

**Differentiation of Exponential and Logarithmic Functions:**

**Differentiation of a Function of a Function:**

Theorem: For any two differentiable functions f(x) and g(x), fog is also differentiable and

(fog)’ (x) = f ’(g (x) ). g ’(x).

**Relation between ****dy/dx**** and ****dx/dy**** :**

**Logarithmic Differentiation:**

- In this section, we will learn to find the derivatives of the functions of the form

[f(x)] ^{g(x)}

We do this by taking the logarithm of both sides and the differentiating both sides.

If y = [f(x)]^{g(x)}

y = [f(x)]g(x) = e^{g(x).log {f(x)}}

**Differentiating of Infinite Series:**

Sometimes the value of y is given as an infinite series and we are asked to find dy/dx. In such cases, we use the fact that if a term is deleted in an infinite series, it remains unchanged.

**Differentiation of Parametric Functions:**

**Differentiation of Determinants:**

**Highlights:**

For continuous functions:

- f(x) + g(x) will be continuous at x = a
- f(x) – g(x) will be continuous at x = a
- f(x) × g(x) will be continuous at x = a
- f(x) / g(x) will be continuous at x = a; provided g(a) ≠0
- d .[f(x)+g(x)] / dx = d . f(x)/dx + d . g(x)/dx

### Discussion of All Exercises of RS Aggarwal Solutions for Class 12 Chapter 7 – Adjoint and Inverse of a Matrix

- The initial exercises especially 10A, 10B, 10C, and 10D questions cover differentiation problems of the given three functions- inverse trigonometric functions, exponential and logarithmic functions in a detailed format.
- In the later exercises, you will learn to differentiate the function of a function, infinite series, parametric functions, and determinants using the processes learned in the initial exercises.
- Solving these questions at the Instasolv platform will boost your skills in approaching a problem in calculus.
- The exercise questions in RS Aggarwal Chapter will also help you recall the differentiation concepts learned by you in your previous classes, and hence, will increase your competence substantially.

### Benefits of RS Aggarwal Solutions for Class 12 Maths Chapter 7 by Instasolv

- The answers by the expert team at Instasolv employ very simple language dedicated to helping you achieve clarity in the subject.
- You will also be able to learn effective time management skills by solving the exercise at Instasolv and become one of the toppers in your class.
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- The solutions are strictly based on the Class 12 CBSE guidelines and therefore, are very reliable.