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# NCERT Solutions class 12 Maths Exercise 5.5

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## NCERT Solutions class 12 Continuity & Differentiability

Differentiate the functions with respect to  in Exercise 1 to 5.

1.

Ans. Let   ……….(i)

Taking logs on both sides, we have

=

[From eq. (i)]

2.

Ans. Let  =   ……….(i)

Taking logs on both sides, we have

[From eq. (i)]

3.

Ans. Let  ……….(i)

Taking logs on both sides, we have

[By Product rule]

=

4.

Ans. Let

Putting  and

……….(i)

Now,

=  ……….(ii)

Again,

……….(iii)

Putting the values from eq. (ii) and (iii) in eq. (i),

5.

Ans. Let  …….(i)

Taking logs on both sides, we have

[From eq. (i)

Differentiate the functions with respect to  in Exercise 6 to 11.

6.

Ans. Let

Putting             and

……….(i)

Now

=  ……….(ii)

Again

……….(iii)

Putting the values from eq. (ii) and (iii) in eq. (i),

7.

Ans. Let  =   where  and

……….(i)

Now

……….(ii)

Again

……….(iii)

Putting the values from eq. (ii) and (iii) in eq. (i),

8.

Ans. Let  =  where  and

……….(i)

Now

……….(ii)

Again

=

=  ……….(iii)

Putting the values from eq. (ii) and (iii) in eq. (i),

9.

Ans. Let

Putting  and , we get

……….(i)

Now

=

…..(ii)

Again

=

……….(iii)

Putting values from eq. (ii) and (iii) in eq. (i),

10.

Ans. Let

Putting  and , we have

……….(i)

Now

=

……….(ii)

Again

……….(iii)

Putting the values from eq. (ii) and (iii) in eq. (i),

11.

Ans. Let

Putting  and , we have

……….(i)

Now

=

……….(ii)

Again

=

……….(iii)

Putting the values from eq. (ii) and (iii) in eq. (i)

,

Find  in the following Exercise 12 to 15

12.

Ans. Given:

where  and

……….(i)

Now

……….(ii)

Again

……….(iii)

Putting values from eq. (ii) and (iii) in eq. (i),

13.

Ans. Given:

14.

Ans. Given:

15.

Ans. Given:

16. Find the derivative of the function given by  and hence

Ans. Given:      ……….(i)

Putting the value of  from eq. (i),

= 8 x 15 = 120

17. Differentiate  in three ways mentioned below:

(i)    by using product rule.

(ii)   by expanding the product to obtain a single polynomial

(iii)  by logarithmic differentiation.

Do they all give the same answer?

Ans. Let  ……….(i)

(i)

……….(ii)

(ii)

……….(iii)

(iii)

[From eq. (i)]

……….(iv)

From eq. (ii), (iii) and (iv), we can say that value of  is same obtained by three different methods.

18. If  and  are functions of  then show that  in two ways – first by repeated application of product rule, second by logarithmic differentiation.

Ans. Given:  and  are functions of

To prove:

(i) By repeated application of product rule:

L.H.S.   =

=

=

=

=

=

= R.H.S  Hence proved.

(ii) By Logarithmic differentiation:

Let

Putting , we get

Hence proved.

## NCERT Solutions class 12 Maths Exercise 5.5

NCERT Solutions Class 12 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 12 Maths includes text book solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 12 Maths have total 20 chapters. 12 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 12 solutions PDF and Maths ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide

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