Chapter 5 Continuity and Differentiability Ex 5.5 Solutions
Question - 11 : - Differentiate the function withrespect to x.
Answer - 11 : - 
Differentiating both sides withrespect to x, we obtain
Differentiating both sides withrespect to x, we obtain
From (1), (2), and (3), we obtain
of function.
Answer - 12 : - The given function is
Let xy = u and yx = v
Then, the function becomes u + v =1
Differentiating both sides withrespect to x, we obtain
Differentiating both sides withrespect to x, we obtain
From (1), (2), and (3), we obtain
Answer - 13 : - The given function is
Taking logarithm on both thesides, we obtain
Differentiating both sides withrespect to x, we obtain
Answer - 14 : - The given function is
Taking logarithm on both thesides, we obtain
Differentiating both sides, weobtain
Answer - 15 : - The given function is
Taking logarithm on both thesides, we obtain
Differentiating both sides withrespect to x, we obtain
and hence find
Answer - 16 : - The given relationship is
Taking logarithm on both thesides, we obtain
Differentiating both sides withrespect to x, we obtain
in three ways mentioned below(i) By using product rule.
(ii) By expanding the product toobtain a single polynomial.
(iii By logarithmicdifferentiation.
Do they all give the same answer?
Answer - 17 : - 
(i)
(ii)
(iii)
Taking logarithm on both thesides, we obtain
Differentiating both sides withrespect to x, we obtain
From the above three observations, it can be concludedthat all the results of are same.
If u, v and w arefunctions of x, then show that
in two ways-first by repeatedapplication of product rule, second by logarithmic differentiation.
Answer - 18 : - Let 
By applying product rule, weobtain
By taking logarithm on both sides of the equation
,
we obtain
Differentiating both sides withrespect to x, we obtain
