** NCERT Solutions for Maths Class 12 Exercise 5.2**

Hello Students! Welcome to **maths-formula.com**. In this post, you will find the complete** ****NCERT Solutions for Maths Class 12 Exercise 5.2**.

You can download the **PDF of NCERT Books Maths Chapter 5** for your easy reference while studying **NCERT Solutions for Maths Class 12 Exercise 5.2**.

Class 12th is a very crucial stage of your student’s life, since you take all important decisions about your career on this stage. Mathematics plays a vital role to take decision for your career because if you are good in mathematics, you can choose engineering and technology field as your career.

**NCERT Solutions for Maths Class 12 Exercise 5.2** helps you to solve each and every problem with step by step explanation which makes you strong in mathematics.

All the schools affiliated with CBSE, follow the NCERT books for all subjects. You can check your syllabus from **NCERT Syllabus for Mathematics Class 12**.

**NCERT Solutions for Maths Class 12 Exercise 5.2** are prepared by the experienced teachers of CBSE board. If you are preparing for JEE Mains and NEET level exams, then it will definitely make your foundation strong.

If you want to recall **All Maths Formulas for Class 12**, you can find it by clicking this link.

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**NCERT Solutions for Maths Class 12 Exercise 5.1**

**NCERT Solutions for Maths Class 12 Exercise 5.3**

**NCERT Solutions for Maths Class 12 Exercise 5.4**

**NCERT Solutions for Maths Class 12 Exercise 5.5**

**NCERT Solutions for Maths Class 12 Exercise 5.6**

**NCERT Solutions for Maths Class 12 Exercise 5.7**

**NCERT Solutions for Maths Class 12 Exercise 5.8**

**NCERT Solutions for Maths Class 12 Exercise 5.2**

**Differentiate the
functions with respect to x in Questions 1 to 8.**

**Maths Class
12 Ex 5.2 Question 1.**

sin (x² + 5)

**Solution:**

Let y = sin (x^{2}
+ 5),

Put x² + 5 = t

Then, y = sin t

= cos (x² + 5) × 2x

= 2x cos (x² + 5)

**Maths Class
12 Ex 5.2 Question 2.**

cos (sin x)

**Solution:**

Let y = cos (sin
x)

Put sin x = t

∴ y = cos t, where t = sin x

**Maths Class
12 Ex 5.2 Question 3.**

sin (ax + b)

**Solution:**

Let y = sin (ax + b)

Put ax + b = t

∴ y = sin t, where t = ax + b

**Maths Class
12 Ex 5.2 Question 4.**

sec (tan (√x))

**Solution:**

Let y = sec (tan (√x))

By chain rule,

**Maths Class
12 Ex 5.2 Question 5.**

**Solution:**

**Maths Class
12 Ex 5.2 Question 6.**

cos x³ . sin² (x^{5})

**Solution:**

Let y = cos x³ .
sin² (x^{5})

**Maths Class
12 Ex 5.2 Question 7.**

**Maths Class
12 Ex 5.2 Question 8.**

cos (√x)

**Solution:**

**Maths Class
12 Ex 5.2 Question 9.**

Prove that the
function *f*given by

*f*(x) = |x – 1|, x ∈ R is not differentiable at x = 1.

**Solution:**

We have *f*(x) = |x – 1|,
x ∈ R

It is known that a
function f is
differentiable at a point x = c in its
domain if both LHD and RHD are finite and equal.

To check the differentiability of the
given function at x = 1,

Since LHD and RHD
at x = 1 are
not equal,

Therefore, f is not differentiable
at x = 1.

**Maths Class
12 Ex 5.2 Question 10.**

Prove that the
greatest integer function defined by f(x) = [x], 0 < x < 3 is not
differential at x = 1 and x = 2.

**Solution:**

We have *f*(x) = [x], 0
< x < 3

It is known that a function *f* is
differentiable at a point x = c in its
domain if both LHD and RHD are finite and equal.

To check the differentiability of the given function at x = 1,

Since LHD and RHD
at x = 1 are
not equal,

Therefore, *f* is not
differentiable at x = 1.

Similarly, *f* is not
differentiable at x = 2.

**NCERT Solutions for Maths Class 12 Exercise 5.1**

**NCERT Solutions for Maths Class 12 Exercise 5.3**

**NCERT Solutions for Maths Class 12 Exercise 5.4**

**NCERT Solutions for Maths Class 12 Exercise 5.5**

**NCERT Solutions for Maths Class 12 Exercise 5.6**