NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 are part of NCERT Solutions for Class 11 Maths. Here we have given NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2.
| Board | CBSE |
| Textbook | NCERT |
| Class | Class 11 |
| Subject | Maths |
| Chapter | Chapter 13 |
| Chapter Name | Limits and Derivatives |
| Exercise | Ex 13.2 |
| Number of Questions Solved | 11 |
| Category | NCERT Solutions |
NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2
Ex 13.2 Class 11 Maths Question 1.
Find the derivative of x2 – 2 at x = 10.
Solution:
let f(x) = x2 – 2
Differentiating (i) with respect to x, we get
f'(x) = 2x
At x = 10, f'(10) = 2(10) = 20.
Ex 13.2 Class 11 Maths Question 2.
Find the derivative of 99x at x = 10.
Solution:
let f(x) = 99x
Differentiating (i) with respect to x, we get
f'(x) = 90
At x = 100, f'(100) = 99.
Ex 13.2 Class 11 Maths Question 3.
Find the derivative of x at x = 10.
Solution:
let f(x) = x
Differentiating (i) with respect to x, we get
f'(x) = 1
At x = 1, f'(1) = 1.
Ex 13.2 Class 11 Maths Question 4.
Find the derivative of the following functions from first principle.
(i) x3 – 27
(ii) (x – 1)(x – 2)
(iii) \(\frac { 1 }{ { x }^{ 2 } } \)
(iv) \(\frac { x+1 }{ x-1 } \)
Solution:
Ex 13.2 Class 11 Maths Question 5.
For the function
Prove that f'(1) = 100f'(0)
Solution:
We have
Ex 13.2 Class 11 Maths Question 6.
Find the derivative of xn + axn-1 + a2xn-2+
…. + an-1x + an for some fixed real number a.
Solution:
Let f(x) = xn + axn-1 + a2xn-2+
…. + an-1x + an
Differentiating (i) with respect to x, we get
f'(x) = nxn-1 + (n – 1)axn-2 + …… + an-1
Ex 13.2 Class 11 Maths Question 7.
For some constants a and b, find the derivative of
(i) (x – a)(x – b)
(ii) (ax2 + b)2
(iii) \(\frac { x-a }{ x-b } \)
Solution:
(i) Let f(x) = (x – a)(x – b) ….(1)
Differentiating (1) with respect to x, we get
f'(x) = (x – a)(x – b)’ + (x – a)’ (x – b)
⇒ f'(x) = (x – a) + (x – b) = 2x – a – b
Ex 13.2 Class 11 Maths Question 8.
Find the derivative \(\frac { { x }^{ n }-{ a }^{ n } }{ x-a } \) for some constant a.
Solution:
Let f(x) = \(\frac { { x }^{ n }-{ a }^{ n } }{ x-a } \) ….(i), where a is a constant.
Differentiating (i) with respect to x, we get
Ex 13.2 Class 11 Maths Question 9.
Find the derivative of
Solution:
(i) Let f(x) = \(2x-\frac { 3 }{ 4 } \) …(1)
Differentiating (i) with respect to x, we get
f'(x) = 2·1 – 0 ⇒ f'(x) = 2.
(ii) Let f(x) = 5x3 + 3x – 1)(x – 1)
Ex 13.2 Class 11 Maths Question 10.
Find the derivative of cos x from first principle.
Solution:
Let f(x) = cos x
Ex 13.2 Class 11 Maths Question 11.
Find the derivative of the following functions:
(i) sin x cos x
(ii) secx
(iii) 5 secx + 4 cosx
(iv) cosecx
(v) 3 cotx + 5 cosecx
(vi) 5sinx – 6 cosx + 7
(vii) 2 tanx – 7 secx.
Solution:
(i) Let f(x) = sin x cos x … (1)
Differentiating (1) with respect to x, we get
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