Hello Students! 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**.

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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 5.2**

**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.

**Related Links:**

**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**