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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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