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RS Aggarwal Class 12 Solutions Chapter-10 Differentiation

RS Aggarwal Solutions

RS Aggarwal Class 12 Solutions Chapter-10 Differentiation

Last updated date: 25th Apr 2024

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Class 12 RS Aggarwal Chapter-10 Differentiation Solutions - Free PDF Download

To better understand Class 12 Chapter 10, students should prepare RS Aggarwal Class 12 Differentiation Solutions and practice to improve their knowledge and clear any doubts that they may have. Maths can be tricky, but RS Aggarwal Class 12 Solutions Maths Chapter 10 offered by Vedantu makes it easy. These solutions will cover all the relevant questions and follow the same pattern as followed in your board examination. When you practice these solutions, it will reduce your fear of appearing in any competitive exam. The solution also helps to clear all your weak areas.

The RS Aggarwal Class 12 Solutions Maths Chapter 10, which is available on this page, is designed in a simple way to tackle the complexities that students face in their advanced Mathematical terminologies and concepts. The solutions should be used to prepare well for the examination. Experts have prepared these to answer the questions in a detailed manner. Once you solve these solutions, you will tackle every difficult question with ease.

Download RS Aggarwal Solutions Class 12 Solutions Chapter 10 in PDF

The Class 12 RS Aggarwal Solutions Differentiation solutions can now be downloaded from the official Vedantu website and are available in PDF format. The solutions make it quick for the student to refer to them on the go. You can download these solutions to any device of your choice. The offline download comes in very handy, especially when you want to prepare for your exam and you do not have an internet connection. You also prefer to keep a hard copy of these.

Differentiation Class 12 RS Aggarwal Solutions

The RS Aggarwal Maths Class 12 Solutions Differentiation is an important concept. Differentiation is a method where you find out the derivative of any function. The process is where you find out any instantaneous change in the rate of the function, which is based on one of the variables. Velocity is the most common example where you find the rate change of displacement concerning time.
If x is a variable and y is another variable, you calculate the rate of change of x with respect to y which is given by dy/dx. This is a general derivative expression which is a function that is represented as f'(x) = dy/dx and here y=f(x) is a function.
Differentiation is a derivative of any function with respect to an independent variable. The differentiation can be applied to calculus that is applied to a measure of function per unit change that happens in the independent variable.
If y = f(x) is a function of x then the rate of change of y when there is per unit change in x is given as dy/dx.
In case the function f(x) goes through an infinitesimal change of h near to the point x then the function derivative is limit→0f(x+h)–f(x)h
Functions are classified as linear and nonlinear. The linear function will vary with a constant rate all through the domain. The rate of change of the function is the same as compared to the rate of change of the function at any point. The rate of change of function will vary from one point to another. In the case of any nonlinear function, the variation in nature depends on the function's nature. Derivation is the rate of change of the function at one point.

There are some important differentiation formats that students should know.

If f(x) = tan (x), then f'(x) = sec2x
If f(x) = cos (x), then f'(x) = -sin x
If f(x) = sin (x), then f'(x) = cos x
If f(x) = ln(x), then f'(x) = 1/x
If f(x) = ex, then f'(x) = ex
If f(x) = xn, where n is any fraction or integer, then f'(x) = nxn−1

If f(x) = k, where k is a constant, then f'(x) = 0

Differentiation Follows Four Rules. These are The Sum and Difference Rules, Product Rule, Quotient Rule and Chain Rule

1. Sum or Difference Rule

If the function is the sum or difference of two functions then, the derivative of the functions is calculated as the sum or difference of the individual functions, i.e.,

If f(x) = u(x) ± v(x)

then, f'(x)=u'(x) ± v'(x)

2. Product Rule

In the product rule, when the function f(x) is the product of any two functions u(x) and v(x), the derivative of the function is,

If f(x)=u(x)×v(x)

then, f′(x)=u′(x)×v(x)+u(x)×v′(x)

3. Derivative of Inverse Function

If the function f(x) is in the form of two functions say u(x)/v(x)

v(x), then the derivative of the function is

If, f(x)=u(x)v(x)

then, f′(x)=u′(x)×v(x)–u(x)×v′(x)

4. Chain Rule

If a function y = f(x) = g(u) and if u = h(x), then the chain rule for differentiation is defined as,

Dy/dx=dy/du×du/dx

Differentiation helps to find the rate of change of a quantity with respect to each other. Some of these are acceleration which is the rate of change of velocity with respect to time
The derivative function gets used to finding the highest or the lowest point in the cure to know what it's turning point is
Differentiation is used to find the normal and tangent to any curve.

Preparation Tips for RS Aggarwal Class 12 Maths Chapter 10

You must practice the exercise well to gain total clarity on the differentiation topic that is covered in your syllabus
The solution lets you understand the topic that enables you to solve questions fast and also approach complex questions
You will not just be able to get good marks but also be able to approach tricky questions
This is one of the best solutions on differentiation that builds on your concepts on this topic.

FAQs on RS Aggarwal Class 12 Solutions Chapter-10 Differentiation

1. What are the Differentiation Formulas for Inverse Trigonometric Functions?

Inverse trigonometry functions are basically the inverse of trigonometric ratios. These inverse trigonometric functions are also called the arcus function, cyclometric function or the anti trigonometric functions and are used to find the value of an angle for a particular trigonometric value. Here are the formulas for derivatives of inverse trigonometric functions.

d/dx (sin−1 x) = 1/ √(1–x2)
d/dx (cos−1 x) = −1/ √(1–x2)
d/dx (tan−1 x) = 1/(1+x2)
d/dx (cot−1 x) = −1/(1+x2)
d/dx (sec−1 x)= 1/ √(|x|x2–1)
d/dx (cosec−1 x)= −1/ √(|x|x2–1)

2. What is the derivative value of a constant value?

Inverse trigonometry functions are basically the inverse of trigonometric ratios. Here are the formulas for derivative of inverse trigonometric functions from the class 12 RS Aggarwal for Chapter 10 Differentiation:

d/dx (sin−1 x) = 1/ √(1–x2)
d/dx (cos−1 x) = −1/ √(1–x2)
d/dx (tan−1 x) = 1/(1+x2)
d/dx (cot−1 x) = −1/d/dx (sec−1 x)= 1/ √(|x|x2–1)
d/dx (cosec−1 x)= −1/ √(|x|x2–1)

The derivative of a constant value is 0. So if f(x) =5 then f’(x) = 0

3. What topics do the exercises in Chapter 10 of Class 12 RS Aggarwal cover?

Chapter 10 Differentiation of class 12 Mathematics RS Aggarwal consists of a total of 10 exercises. These exercises help the students to thoroughly revise all the concepts taught in the chapter and give them the necessary practice. The first four exercises of chapter 10 contain questions pertaining to differentiation problems of mainly 3 functions which are inverse trigonometric functions, exponential functions and logarithmic functions. The exercises that follow teach the students about differentiating the function of a function and other concepts such as infinite series, parametric functions and determinants.

4. Why should I download RS Aggarwal Solutions for Class 12 chapter 10 Differentiation from Vedantu?

Solutions for class 12 RS Aggarwal by Vedantu has several benefits which only help towards making the exam preparation of students a simpler process. These solutions are first of all, available to download and therefore students can use them on any divide based on their convenience even offline. The answers are put forward by the expert Vedantu team in a very easy to understand language which makes the concepts very clear to the students. The questions are answered in detail so as to get rid of any lingering doubts students might have and also give them a detailed knowledge of the same.

5. Which unit does Chapter 10 of RS Aggarwal fall under in the class 12 mathematics CBSE syllabus?

Chapter 10 of RS Aggarwal for Class 12 teaches the concept of differentiation to the students which are similar to chapter 9 of Class 12 CBSE syllabus Differential Equations and therefore, fall under Unit III of Calculus. The unit further contains 4 other chapters such as Application of Integrals, Integrals, Applications of Derivatives, and Continuity and Differentiability. Chapter 9 of the NCERT textbook for Class 12 covers topics such as the definition and order and degree of differential equations as well as formation, methods of solution, and solutions of linear differential equations.