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Install NowNCERT Solutions class 12 Maths Exercise 5.5 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 Maths chapter wise NCERT solution for Maths part 1 and Maths part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.

**Download NCERT solutions for Continuity and Differentiability as PDF.**

## 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

## CBSE App for Class 12

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