Question 1:
Find the second order derivatives of the function.
Answer:
Let
Then,
Question 2:
Find the second order derivatives of the function.
Answer:
Let
Then,
Question 3:
Find the second order derivatives of the function.
Answer:
Let
Then,
Question 4:
Find the second order derivatives of the function.
Answer:
Let
Then,
Question 5:
Find the second order derivatives of the function.
Answer:
Let
Then,
Question 6:
Find the second order derivatives of the function.
Answer:
Let
Then,
Question 7:
Find the second order derivatives of the function.
Answer:
Let
Then,
Question 8:
Find the second order derivatives of the function.
Answer:
Let
Then,
Question 9:
Find the second order derivatives of the function.
Answer:
Let
Then,
Question 10:
Find the second order derivatives of the function.
Answer:
Let
Then,
Question 11:
If , prove that
Answer:
It is given that,
Then,
Hence, proved.
Question 12:
If find in terms of y alone.
Answer:
It is given that,
Then,
Question 13:
If , show that
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.