NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE

Continuity & Differentiability

Question 1: Find the second order derivatives of the function.

Answer
Let y =
Then,

Question 2: Find the second order derivatives of the function. x²⁰

Answer
Let y = x²⁰
Then,

Question 3: Find the second order derivatives of the function. x.cos x

Answer
Let y = x.cos x
Then,

Question 4: Find the second order derivatives of the function. log x

Answer
Let y = log x
Then,

Question 5: Find the second order derivatives of the function. x³ log x

Answer
Let y = x³ log x
Then,

Question 6: Find the second order derivatives of the function. 

Answer

Let y =

Question 7: Find the second order derivatives of the function.

Answer
Let y =
Then,

Question 8: Find the second order derivatives of the function.

Answer
Let y =
Then,

Question 9: Find the second order derivatives of the function.

Answer
Let y =
Then,

Question 10: Find the second order derivatives of the function.

Answer
Let y =
Then,

Question 11: If 

Answer
It is given that,
Then,

Hence, proved.

Question 12:
 If    in terms of y alone.

Answer
It is given that,
Then,

Question 13:
 If 

Answer
It is given that, 
Then,

Hence, proved.

Question 14:
 If , show that  

Answer
It is given that,
Then,

Hence, proved.

Question 15:
 If  , show that 

Answer
It is given that,
Then,

Hence, proved.

Question 16:
 If  , show that 

Answer
The given relationship is

Taking logarithm on both the sides, we obtain

Differentiating this relationship with respect to x, we obtain

Hence, proved.

Question 17:
 If , show that 

Answer
The given relationship is
Then,

 
Hence, proved.