Exercise 5.7
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NCERT Solutions class 12 Continuity & Differentiability
Find the second order derivatives of the functions given in Exercises 1 to 5.
1. 
Ans. Let 
2. 
Ans. Let 
3. 
Ans. Let 
= 
= 
= 
= 
= 
= 
4. 
Ans. Let 
= 
5. 
Ans. Let 
= 
= 
= 
= 
= 
= 
= 
= 
= 
Find the second order derivatives of the functions given in Exercises 6 to 10.
6. 
Ans. Let 
= 
= 
= 
= 
= 
= 
7. 
Ans. Let 
= 
= 
= 
= 
= 
= 
8. 
Ans. Let 
= 
= 
= 
9. 
Ans. Let 
= 
= 
= 
= 
10. 
Ans. Let 
= 
= 
= 
= 
= 
11. If 
prove that 
Ans. Let 
…….(i)
= 
= 
[From eq. (i)]
12. If 
Find 
in terms of 
alone.
Ans. Given: 
……….(i)
= 
[From eq. (i)]
= 
……….(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.=
= 
= 
= 0
= R.H.S. Hence proved.
NCERT Solutions class 12 Maths Exercise 5.7
15. If 
show that 
Ans. Given: 
……….(i)
= 
= 
= 
[From eq. (i)]
= Hence proved.
NCERT Solutions class 12 Maths Exercise 5.7
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.
NCERT Solutions class 12 Maths Exercise 5.7
17. If 
show that 
Ans. Given: 
……….(i)
And 
= 
Again differentiating both sides w.r.t. 
Hence proved.