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# NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE

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Continuity & Differentiability

Question 1: Differentiate the function with respect to x.  Question 2: Differentiate the function with respect to x. Let y = 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. Let y = 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. xx - 2sinx

Let y =  u = xx
Taking logarithm on both the sides, we obtain Differentiating both sides with respect to x, we obtain Question 5: Differentiate the function with respect to x. Let y = 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.  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. Let y =  Differentiating both sides with respect to x, we obtain Differentiating both sides with respect to x, we obtain Question 8: Differentiate the function with respect to x. Let y =  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. Let y =  Differentiating both sides with respect to x, we obtain Question 10: Differentiate the function with respect to x. Let y =  Differentiating both sides with respect to x, we obtain Differentiating both sides with respect to x, we obtain Question 11: Differentiate the function with respect to x.  Differentiating both sides with respect to x, we obtain  Differentiating both sides with respect to x, we obtain Question 12:
Find of function . Differentiating both sides with respect to x, we obtain Question 13:

Find  Differentiating both sides with respect to x, we obtain Question 14:
Find of function . Differentiating both sides, we obtain Question 15:
Find of function . Differentiating both sides with respect to x, we obtain Question 16:
Find the derivative of the function given by and
hence find .

The given relationship is Taking logarithm on both the sides, we obtain Differentiating both sides with respect to x, we obtain Question 17:
Differentiate in three ways mentioned below
(i) By using product rule.
(ii) By expanding the product to obtain a single polynomial.
(iii By logarithmic differentiation.
Do they all give the same answer?

Let y = (i) (ii) ( iii) Taking logarithm on both the sides, we obtain Differentiating both sides with respect to x, we obtain From the above three observations, it can be concluded that all the results of are same.

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.

Let By applying product rule, we obtain The document NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE is a part of the JEE Course Mathematics For JEE.
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## Mathematics For JEE

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## Mathematics For JEE

130 videos|359 docs|306 tests

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