# NCERT Solutions class 12 Maths Exercise 5.7 (Ex 5.7) Chapter 5 Continuity and Differentiability

## NCERT Solutions for Class 12 Maths Exercise 5.7 Chapter 5 Continuity and Differentiability – FREE PDF Download

Free PDF download of NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.7 (Ex 5.7) and all chapter exercises at one place prepared by expert teacher as per NCERT (CBSE) books guidelines. Class 12 Maths Chapter 5 Continuity and Differentiability Exercise 5.7 Questions with Solutions to help you to revise complete Syllabus and Score More marks.

# NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Exercise 5.7 (Ex 5.7)

Find the second order derivatives of the functions given in Exercises 1 to 5.

1.

Ans.  Let

Ans. Let

Ans. Let

=

Ans. Let

=

Ans. Let

### Find the second order derivatives of the functions given in Exercises 6 to 10.

6.

Ans. Let

=ex[5(sin5x)×5+(cos5x)×5]+(5cos5x+sin5x)ex=ex[5(−sin5x)×5+(cos5x)×5]+(5cos5x+sin5x)ex

### 7.

Ans. Let

e6x(3sin3x+6cos3x)e6x(−3sin⁡3x+6cos⁡3x)

Ans. Let

=

### 9.

Ans.  Let

[x.1x+logx×1](xlogx)2−[x.1x+log⁡x×1](xlog⁡x)2

[1+logx](xlogx)2−[1+log⁡x](xlog⁡x)2

Ans. Let

=

### 11. If  prove that

Ans. Let   …….(i)

=  [From eq. (i)]

Ans. Given:

……….(i)

[From eq. (i)]

……….(ii)

[From eq. (ii)]

### 13. If  show that

Ans. Given:      ….(i)

=

Now

[From eq. (i)]

Hence proved.

### 14. If  show that

Ans.  Given:     ….(i)

To prove:

….(ii)

Again
….(iii)

Now,   L.H.S.=
Am2emx+Bn2enx(m+n)(Amemx+Bnenx)+mn(Aemx+Benx)Am2emx+Bn2enx−(m+n)(Amemx+Bnenx)+mn(Aemx+Benx)

Am2emx+Bn2enxAm2emxBmnenxAmnemxBn2enx+Amnemx+BmnenxAm2emx+Bn2enx−Am2emx−Bmnenx−Amnemx−Bn2enx+Amnemx+Bmnenx

= 0

= R.H.S.            Hence proved.

### 15. If  show that

Ans. Given: ……….(i)

= 500(7)e7x600(7)e7x500(7)e7x−600(7)e−7x

d2ydx2=500(7)e7x(7)600(7)e7x(7)d2ydx2=500(7)e7x(7)−600(7)e−7x(−7) = 500(49)e7x+600(49)e7x500(49)e7x+600(49)e−7x

d2ydx2=49[500e7x+600e7x]d2ydx2=49[500e7x+600e−7x]

[From eq. (i)]

=   Hence proved.

### 16. If  show that

Ans. Given:

Taking log on both sides,

=

And

Now, L.H.S. =

And R.H.S. =

L.H.S. = R.H.S.         Hence proved.

### 17. If  show that

Ans. Given:       ……….(i)

And

Again  differentiating both sides w.r.t.

Hence proved.