JEE  >  Mathematics For JEE  >  NCERT Solutions Exercise 5.5: Continuity & Differentiability

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

1 Crore+ students have signed up on EduRev. Have you? Download the App

Continuity & Differentiability 

Question 1: Differentiate the function with respect to x.

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


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

Question 2: Differentiate the function with respect to x.

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


Answer

Let y = NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Taking logarithm on both the sides, we obtain

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

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

Differentiating both sides with respect to x, we obtain 

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

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

Question 3: Differentiate the function with respect to x. NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE

Answer

Let y = NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Taking logarithm on both the sides, we obtain

NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Differentiating both sides with respect to x, we obtain
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE

Question 4: Differentiate the function with respect to x. xx - 2sinx


Answer

Let y = NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE

NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
u = xx
Taking logarithm on both the sides, we obtain

NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Differentiating both sides with respect to x, we obtain

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

 

Question 5: Differentiate the function with respect to x.

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

Answer

Let y = NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Taking logarithm on both the sides, we obtain

NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Differentiating both sides with respect to x, we obtain
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE

 


Question 6: Differentiate the function with respect to x.

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


Answer

NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Differentiating both sides with respect to x, we obtain

NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Differentiating both sides with respect to x, we obtain

NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Therefore, from (1), (2), and (3), we obtain

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



Question 7: Differentiate the function with respect to x.

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

Answer

Let y = NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Differentiating both sides with respect to x, we obtain
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Differentiating both sides with respect to x, we obtain
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE


Question 8: Differentiate the function with respect to x.

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

Answer

Let y = NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE

Differentiating both sides with respect to x, we obtain

NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Therefore, from (1), (2), and (3), we obtain

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


Question 9: Differentiate the function with respect to x.

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


Answer
Let y = NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE

NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Differentiating both sides with respect to x, we obtain
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE

Question 10: Differentiate the function with respect to x.

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


Answer

Let y = NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE

NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Differentiating both sides with respect to x, we obtain
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Differentiating both sides with respect to x, we obtain
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE


Question 11: Differentiate the function with respect to x.
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE

Answer

NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Differentiating both sides with respect to x, we obtain

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

NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Differentiating both sides with respect to x, we obtain
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
 

Question 12:
 Find 
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE of function NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE.


Answer
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Differentiating both sides with respect to x, we obtain

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


Question 13:

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


Answer
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Differentiating both sides with respect to x, we obtain

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



Question 14:
 Find NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE of function NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE .


Answer
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Differentiating both sides, we obtain

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



Question 15:
 Find 
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE  of function NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE.


Answer
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Differentiating both sides with respect to x, we obtain
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE


Question 16:
 Find the derivative of the function given by  
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE  and
 hence find 
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE.


Answer
The given relationship is NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Taking logarithm on both the sides, we obtain

NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Differentiating both sides with respect to x, we obtain

NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Question 17:
 Differentiate 
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE  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?


Answer

Let y = NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
(i)

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


(ii)

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


( iii) NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE

Taking logarithm on both the sides, we obtain

NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
Differentiating both sides with respect to x, we obtain

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

From the above three observations, it can be concluded that all the results of NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE  are same.

 Question 18: If u, v and w are functions of x, then show that

NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
in two ways-first by repeated application of product rule, second by logarithmic
 differentiation.


Answer
Let NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE
By applying product rule, we obtain
NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE

The document NCERT Solutions Exercise 5.5: Continuity & Differentiability | Mathematics For JEE is a part of the JEE Course Mathematics For JEE.
All you need of JEE at this link: JEE
130 videos|359 docs|306 tests
130 videos|359 docs|306 tests
Download as PDF

Download free EduRev App

Track your progress, build streaks, highlight & save important lessons and more!
(Scan QR code)

Related Searches

Objective type Questions

,

practice quizzes

,

Summary

,

Extra Questions

,

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

,

Important questions

,

Free

,

Exam

,

Viva Questions

,

pdf

,

Sample Paper

,

mock tests for examination

,

study material

,

Semester Notes

,

Previous Year Questions with Solutions

,

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

,

shortcuts and tricks

,

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

,

MCQs

,

video lectures

,

past year papers

,

ppt

;