NCERT Solutions for Class 12 Maths Chapter 5 – Continuity and Differentiability Ex 5.5
Page No 178:
Question 1:
Differentiate the function with respect to x.
Answer:
Taking logarithm on both the sides, we obtain
Differentiating both sides with respect to x, we obtain
Question 2:
Differentiate the function with respect to x.
Answer:
Taking logarithm on both the sides, we obtain
Differentiating both sides with respect to x, we obtain
Question 3:
Differentiate the function with respect to x.
Answer:
Taking logarithm on both the sides, we obtain
Differentiating both sides with respect to x, we obtain
Question 4:
Differentiate the function with respect to x.
Answer:
u = xx
Taking logarithm on both the sides, we obtain
Differentiating both sides with respect to x, we obtain
v = 2sin x
Taking logarithm on both the sides with respect to x, we obtain
Differentiating both sides with respect to x, we obtain
Question 5:
Differentiate the function with respect to x.
Answer:
Taking logarithm on both the sides, we obtain
Differentiating both sides with respect to x, we obtain
Question 6:
Differentiate the function with respect to x.
Answer:
Differentiating both sides with respect to x, we obtain
Differentiating both sides with respect to x, we obtain
Therefore, from (1), (2), and (3), we obtain
Question 7:
Differentiate the function with respect to x.
Answer:
u = (log x)x
Differentiating both sides with respect to x, we obtain
Differentiating both sides with respect to x, we obtain
Therefore, from (1), (2), and (3), we obtain
Question 8:
Differentiate the function with respect to x.
Answer:
Differentiating both sides with respect to x, we obtain
Therefore, from (1), (2), and (3), we obtain
Question 9:
Differentiate the function with respect to x.
Answer:
Differentiating both sides with respect to x, we obtain
Differentiating both sides with respect to x, we obtain
From (1), (2), and (3), we obtain
Question 10:
Differentiate the function with respect to x.
Answer:
Differentiating both sides with respect to x, we obtain
Differentiating both sides with respect to x, we obtain
From (1), (2), and (3), we obtain
Question 11:
Differentiate the function with respect to x.
Answer:
Differentiating both sides with respect to x, we obtain
Differentiating both sides with respect to x, we obtain
From (1), (2), and (3), we obtain
Question 12:
Find 
of function.
of function.
Answer:
The given function is
Let xy = u and yx = v
Then, the function becomes u + v = 1
Differentiating both sides with respect to x, we obtain
Differentiating both sides with respect to x, we obtain
From (1), (2), and (3), we obtain
Question 13:
Find 
of function.
of function.
Answer:
The given function is
Taking logarithm on both the sides, we obtain
Differentiating both sides with respect to x, we obtain
Question 14:
Find 
of function.
of function.
Answer:
The given function is
Taking logarithm on both the sides, we obtain
Differentiating both sides, we obtain
Question 15:
Find 
of function.
of function.
Answer:
The given function is
Taking logarithm on both the sides, we obtain
Differentiating both sides with respect to x, we obtain
Question 16:
Find the derivative of the function given by
and hence find
.
and hence find.Answer:
The given relationship is
Taking logarithm on both the sides, we obtain
Differentiating both sides with respect to x, we obtain
Page No 179:
Question 18:
If u, v and w are functions of x, then show that
in two ways-first by repeated application of product rule, second by logarithmic differentiation.
Answer:
Let 
By applying product rule, we obtain
By taking logarithm on both sides of the equation
, we obtain
, we obtain
Differentiating both sides with respect to x, we obtain
