RD Sharma Solutions Class 11 Maths Chapter 30 – Derivatives: Derivatives are considered to be among the most important chapters of Class 11 mathematics. You will learn to use limits (which you have studied in the previous chapter) with derivatives. This chapter will also help you in your Class 12 Maths exam prep. Therefore, it is important to get clear with the concepts present in this chapter. Prepare RD Sharma Solutions Class 11 Maths Chapter 30 for better results.
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RD Sharma Solutions Class 11 Maths Chapter 30
Exercise-wise RD Sharma Solutions Class 11 Maths Chapter 30 – Derivatives
RD Sharma Solutions Class 11 Maths Chapter 30 Exercise-30.1
Exercise 30.1 is all about derivatives at a point. Throughout this chapter, it will be assumed that a given function f(x) is differentiable at every point in its domain i.e. exists for all c in its domain.
In this exercise, you will encounter questions like these, Find the derivative of f(x) = 3x at x=2.
This exercise is super easy. Once you cross this hurdle of solving basic derivatives you can move ahead with further exercises.
RD Sharma Solutions Class 11 Maths Chapter 30 Exercise-30.2
Exercise – 30.2 covers some more important topics of derivatives. It includes finding derivatives of a function, and differentiation from the first principle.
This exercise will add more when you go for other exercises. Go through each question and concept carefully while solving questions of Exercise – 30.2. RD Sharma solutions will help you understand and solve questions effectively.
RD Sharma Solutions Class 11 Maths Chapter 30 Exercise-30.3
Every exercise adds up one extra concept and finally mixes all of them to let students know how to proceed when a question comes to test all the concepts together.
Exercise – 30.3 introduces students to fundamental rules for differentiation. There are different theorems for the same. All you need to do is to understand why it is the way it is. Once you understand them it would be easy for you to solve questions.
RD Sharma Solutions Class 11 Maths Chapter 30 Exercise-30.4
Exercise – 30.4 covers only one concept i.e. Product rule for differentiation.
This rule says, Derivative of the product of two functions= [(First Function)* (Derivative of 2nd function) + (Second function)*(Derivative of first function)]
The second theorem is about the Generalization of the product rule.
RD Sharma Solutions Class 11 Maths Chapter 30 Exercise-30.5
Exercise – 30.5 is all about using all the concepts covered till 30.4. This exercise will give you sufficient practice for using the concepts together. Along with it, there will be the quotient rule for differentiation.
Access RD Sharma Solutions Class 11 Maths Chapter 30
EXERCISE 30.1 PAGE NO: 30.3
1. Find the derivative of f(x) = 3x at x = 2
Solution:
Given:
f(x) = 3x
By using the derivative formula,
2. Find the derivative of f(x) = x2 – 2 at x = 10
Solution:
Given:
f(x) = x2 – 2
By using the derivative formula,
= 0 + 20 = 20
Hence,
Derivative of f(x) = x2 – 2 at x = 10 is 20
3. Find the derivative of f(x) = 99x at x = 100.
Solution:
Given:
f(x) = 99x
By using the derivative formula,
4. Find the derivative of f(x) = x at x = 1
Solution:
Given:
f(x) = x
By using the derivative formula,
5. Find the derivative of f(x) = cos x at x = 0
Solution:
Given:
f(x) = cos x
By using the derivative formula,
6. Find the derivative of f(x) = tan x at x = 0
Solution:
Given:
f(x) = tan x
By using the derivative formula,
7. Find the derivatives of the following functions at the indicated points:
(i) sin x at x = π/2
(ii) x at x = 1
(iii) 2 cos x at x = π/2
(iv) sin 2xat x = π/2
Solution:
(i) sin x at x = π/2
Given:
f (x) = sin x
By using the derivative formula,
[Since it is of indeterminate form, let us try to evaluate the limit.]
We know that 1 – cos x = 2 sin2(x/2)
(ii) x at x = 1
Given:
f (x) = x
By using the derivative formula,
(iii) 2 cos x at x = π/2
Given:
f (x) = 2 cos x
By using the derivative formula,
(iv) sin 2xat x = π/2
Solution:
Given:
f (x) = sin 2x
By using the derivative formula,
[Since it is of indeterminate form, we shall apply the sandwich theorem to evaluate the limit.]
Now, multiply the numerator and denominator by 2, and we get
Important Topics from RD Sharma Solutions Class 11 Maths Chapter 30- Derivatives
The chapter is not very simple, it requires a lot of practice and patience.
The important topics are listed below:
- Product rule
- Division Rule
- Quotient Rule for Differentiation
Key Take Away from Class11 Maths Chapter 30- Derivatives RD Sharma Solutions
- Don’t mug up things because it’s important to understand the concepts.
- Consider this book as a help book.
- Go step-by-step while solving questions.
RD Sharma Solutions Class11 Maths Chapter 30
If you are done with this much, it is sufficient for Chapter 30. Once done, it becomes easy for you to solve any type of question. Do let us know if you have any queries about the chapter. We would love to answer all your queries. All the best for your CBSE class 11 examinations.
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