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NCERT Solutions for Class 11 Maths Chapter 13: Limits and Derivatives Exercise 13.2-NCERT Solutions for Exercise 13.2 Class 11 Maths chapter 13 discuss derivatives and the questions related to them. The derivative is an important concept as the field of Science, Commerce and Engineering are concerned. So understanding the basics of derivatives is important. Exercise 13.2 Class 11 Maths helps to understand the basics of derivatives.
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NCERT solutions for Class 11 Maths Chapter 13 Exercise 13.2 solve questions from the definition of the derivative, algebra of derivative functions and Class 11 Maths chapter 13 exercise 13.2 presents questions from derivative of trigonometric and polynomial functions. The basic derivative ideas used to solve the Class 11th Maths chapter 13 exercise 13.2 are also helpful in NCERT syllabs Class 11 and 12 Physics and Chemistry also. With Class 11 Maths chapter 13 exercise 13.2, the following exercise is also present in the chapter limits and derivatives. All the solutions including ex 13.2 class 11 are written and prepared by subject experts at Careers360 in a very easy-to-understand language. Additionally, PDF formats of the solutions are available so that students can access them anytime without incurring any charges.
**In the CBSE Syllabus for the academic year 2023-24, this chapter has been renumbered as Chapter 12.
Answer:
F(x)=
Now, As we know, The derivative of any function at x is
The derivative of f(x) at x = 10:
Question:2 Find the derivative of x at x = 1.
Answer:
Given
f(x)= x
Now, As we know, The derivative of any function at x is
The derivative of f(x) at x = 1:
(Answer)
Question:3 Find the derivative of 99x at x = l00.
Answer:
f(x)= 99x
Now, As we know, The derivative of any function at x is
The derivative of f(x) at x = 100:
Question:4 (i) Find the derivative of the following functions from first principle.
Answer:
Given
f(x)=
Now, As we know, The derivative of any function at x is
Question:4.(ii) Find the derivative of the following function from first principle.
Answer:
f(x)=
Now, As we know, The derivative of any function at x is
(Answer)
Question:4(iii) Find the derivative of the following functions from first principle.
Answer:
f(x)=
Now, As we know, The derivative of any function at x is
(Answer)
Question:4(iv) Find the derivative of the following functions from first principle.
Answer:
Given:
Now, As we know, The derivative of any function at x is
Question:5 For the function Prove that f '(1) =100 f '(0).
Answer:
As we know, the property,
applying that property we get
Now.
So,
Here
Hence Proved.
Question:6 Find the derivative of for some fixed real number a.
Answer:
Given
As we know, the property,
applying that property we get
Question:7(i) For some constants a and b, find the derivative of
Answer:
Given
As we know, the property,
and the property
applying that property we get
Question:7(ii) For some constants a and b, find the derivative of
Answer:
Given
As we know, the property,
and the property
applying those properties we get
Question:7(iii) For some constants a and b, find the derivative of
Answer:
Given,
Now As we know the quotient rule of derivative,
So applying this rule, we get
Hence
Question:8 Find the derivative of for some constant a.
Answer:
Given,
Now As we know the quotient rule of derivative,
So applying this rule, we get
Hence
Question:9(i) Find the derivative of
Answer:
Given:
As we know, the property,
and the property
applying that property we get
Question:9(ii) Find the derivative of
Answer:
Given.
As we know, the property,
and the property
applying that property we get
Question:9(iii) Find the derivative of
Answer:
Given
As we know, the property,
and the property
applying that property we get
Question:9(iv) Find the derivative of
Answer:
Given
As we know, the property,
and the property
applying that property we get
Question:9(v) Find the derivative of
Answer:
Given
As we know, the property,
and the property
applying that property we get
Question:9(vi) Find the derivative of
Answer:
Given
As we know the quotient rule of derivative:
and the property
So applying this rule, we get
Hence
Question:10 Find the derivative of from first principle.
Answer:
Given,
f(x)=
Now, As we know, The derivative of any function at x is
Question:11(i) Find the derivative of the following functions:
Answer:
Given,
f(x)=
Now, As we know the product rule of derivative,
So, applying the rule here,
Question:11(ii) Find the derivative of the following functions:
Answer:
Given
Now As we know the quotient rule of derivative,
So applying this rule, we get
Question:11 (iii) Find the derivative of the following functions:
Answer:
Given
As we know the property
Applying the property, we get
Question:11(iv) Find the derivative of the following functions:
Answer:
Given :
Now As we know the quotient rule of derivative,
So applying this rule, we get
Question:11(v) Find the derivative of the following functions:
Answer:
Given,
As we know the property
Applying the property,
Now As we know the quotient rule of derivative,
So applying this rule, we get
Question:11(vi) Find the derivative of the following functions:
Answer:
Given,
Now as we know the property
So, applying the property,
Question:11(vii) Find the derivative of the following functions:
Answer:
Given
As we know the property
Applying this property,
Most of the questions in exercise 13.2 Class 11 Maths are related to the derivative of polynomial functions. There are eleven questions solved under NCERT solutions for Class 11 Maths chapter 13 exercise 13.2. Questions 10 and 11 of Class 11 Maths chapter 13 exercise 13.2 asks to find the derivative of some trigonometric functions. Derivatives are such concepts that require good practice since these are frequently used in the field of science and technology, engineering, economics etc.
Also Read| Limits And Derivatives Class 11 Notes
As mentioned above derivatives are used in the subjects physics and chemistry and maths of Class 11 and also. So practising exercise 13.2 Class 11 Maths is crucial to get a good idea of concepts.
All the questions listed in the Class 11 Maths chapter 13 exercise 13.2 are important and may get questions from the exercise for Class 11 final exams.
Complete Exercise Coverage: The class 11 maths ex 13.2 solutions encompass all exercises and problems in Exercise 13.2 of the Class 11 Mathematics textbook.
Step-by-Step Solutions: The ex 13.2 class 11 solutions are presented in a clear, step-by-step format, aiding in understanding and application of problem-solving methods.
Clarity and Precision: Written with clarity and precision, ensuring easy comprehension of mathematical concepts and techniques.
Proper Mathematical Notation: Utilizes appropriate mathematical notations and terminology to enhance fluency in mathematical language.
Conceptual Understanding: Class 11 ex 13.2 solutions aim to deepen conceptual understanding rather than promoting rote memorization, encouraging critical thinking.
Free Accessibility: 11th class maths exercise 13.2 answers are typically available free of charge, providing an accessible resource for self-study.
Supplementary Learning Tool: Serves as a supplementary resource to complement classroom instruction and support exam preparation.
Homework and Practice: Students can use these class 11 ex 13.2 solutions to cross-verify their work, practice problem-solving, and enhance overall mathematical skills.
Also, see-
The value of f(x) at 100 =8000
The derivative of 80x is 80 which is a constant
The derivative of 80x^2=160x and the value at 100=16000
Sec^2x
The derivative of ‘a’ =0 since ‘a’ is a constant
Since the rate of change of constant =0, the derivative =0
11 questions are solved from exercise 13.2 Class 11 Maths
Definition of derivative, derivative of polynomial and trigonometric functions.
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