NCERT Solutions Miscellaneous Exercise: Continuity and Differentiability | Mathematics (Maths) Class 12 - JEE PDF Download

 Page 1


 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
Miscellaneous Exercise                                              Page No: 191 
 
Differentiate with respect to x the functions in Exercises 1 to 11. 
1.  
Solution:  Consider  
  
 
   
  
2.  
Solution:  Consider   
or y =  
  
   
=  
3.  
Solution:  Consider  
 
Taking log both the sides, we get 
 
  
Page 2


 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
Miscellaneous Exercise                                              Page No: 191 
 
Differentiate with respect to x the functions in Exercises 1 to 11. 
1.  
Solution:  Consider  
  
 
   
  
2.  
Solution:  Consider   
or y =  
  
   
=  
3.  
Solution:  Consider  
 
Taking log both the sides, we get 
 
  
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
  
Derivate above function: 
  
  
  
  
  
 (using value of y) 
4.  
Solution:  Consider   
or  y =  
 
Apply derivation: 
  
=  
 
Page 3


 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
Miscellaneous Exercise                                              Page No: 191 
 
Differentiate with respect to x the functions in Exercises 1 to 11. 
1.  
Solution:  Consider  
  
 
   
  
2.  
Solution:  Consider   
or y =  
  
   
=  
3.  
Solution:  Consider  
 
Taking log both the sides, we get 
 
  
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
  
Derivate above function: 
  
  
  
  
  
 (using value of y) 
4.  
Solution:  Consider   
or  y =  
 
Apply derivation: 
  
=  
 
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
=  
5.  
Solution:  Consider  
 
Apply derivation: 
 
  [Using Quotient Rule] 
  
  
 =  
Page 4


 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
Miscellaneous Exercise                                              Page No: 191 
 
Differentiate with respect to x the functions in Exercises 1 to 11. 
1.  
Solution:  Consider  
  
 
   
  
2.  
Solution:  Consider   
or y =  
  
   
=  
3.  
Solution:  Consider  
 
Taking log both the sides, we get 
 
  
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
  
Derivate above function: 
  
  
  
  
  
 (using value of y) 
4.  
Solution:  Consider   
or  y =  
 
Apply derivation: 
  
=  
 
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
=  
5.  
Solution:  Consider  
 
Apply derivation: 
 
  [Using Quotient Rule] 
  
  
 =  
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
   
=  
6.  
Solution:  Consider  ……….(i) 
 
Reduce the functions into simplest form, 
 
  
=  =  
And  
=  =  
Now, we are available with the equation below: 
   
Page 5


 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
Miscellaneous Exercise                                              Page No: 191 
 
Differentiate with respect to x the functions in Exercises 1 to 11. 
1.  
Solution:  Consider  
  
 
   
  
2.  
Solution:  Consider   
or y =  
  
   
=  
3.  
Solution:  Consider  
 
Taking log both the sides, we get 
 
  
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
  
Derivate above function: 
  
  
  
  
  
 (using value of y) 
4.  
Solution:  Consider   
or  y =  
 
Apply derivation: 
  
=  
 
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
=  
5.  
Solution:  Consider  
 
Apply derivation: 
 
  [Using Quotient Rule] 
  
  
 =  
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
   
=  
6.  
Solution:  Consider  ……….(i) 
 
Reduce the functions into simplest form, 
 
  
=  =  
And  
=  =  
Now, we are available with the equation below: 
   
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
=  
  
 =  
Apply derivation: 
 
  
7.  
Solution:  Consider  ……….(i) 
 
Taking log both sides: 
  =  
Apply derivation: 
 
  
  
  
=