NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.4

In this chapter, we provide NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.4 for English medium students, Which will very helpful for every student in their exams. Students can download the latest NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.4 pdf, free NCERT solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.4 book pdf download.

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Exc  5.4

Differentiate the following w.r.t.x:

Ex 5.4 Class 12 Maths Question 1.
frac { { e }^{ x } }{ sinx }
Solution:
y=frac { { e }^{ x } }{ sinx }
forquad y=frac { u }{ v } ,
frac { dy }{ dx } =frac { { e }^{ x }{ sin }x-{ e }^{ x }cosx }{ { sin }^{ 2 }x }
orfrac { dy }{ dx } =frac { { e }^{ x }{ sin }x-{ e }^{ x }cosx }{ { sin }^{ 2 }x } ,wherequad xneq npi ,xin z

Ex 5.4 Class 12 Maths Question 2.
{ e }^{ { sin }^{ -1 }x }
Solution:
{ e }^{ { sin }^{ -1 }x }
y={ e }^{ { sin }^{ -1 }x }
x=sint
therefore y={ e }^{ t },frac { dt }{ dx } =frac { 1 }{ sqrt { 1-{ x }^{ 2 } } } ,frac { dy }{ dt } ={ e }^{ t }
therefore frac { dy }{ dx } =frac { dy }{ dt } .frac { dt }{ dx } ={ e }^{ t }.frac { 1 }{ sqrt { { 1- }x^{ 2 } } } =frac { { e }^{ { sin }^{ -1 }x } }{ sqrt { 1-{ x }^{ 2 } } }

Ex 5.4 Class 12 Maths Question 3.
{ e }^{ { x }^{ 3 } }=y
Solution:
{ e }^{ { x }^{ 3 } }=y
Putquad { x }^{ 3 }=tquad therefore quad y={ e }^{ t },frac { dy }{ dt } ={ e }^{ t },frac { dt }{ dx } ={ 3x }^{ 2 }
therefore frac { dy }{ dx } =frac { dy }{ dt } times frac { dt }{ dx } ={ e }^{ t }times { 3x }^{ 2 }={ 3x }^{ 2 }{ e }^{ { x }^{ 3 } }

Ex 5.4 Class 12 Maths Question 4.
sinleft( { tan }^{ -1 }{ e }^{ -x } right) =y
Solution:
sinleft( { tan }^{ -1 }{ e }^{ -x } right) =y
frac { dy }{ dx } =cosleft( { tan }^{ -1 }{ e }^{ -x } right) frac { d }{ dx } left( { tan }^{ -1 }{ e }^{ -x } right)
=cosleft( { tan }^{ -1 }{ e }^{ -x } right) frac { 1 }{ 1+{ e }^{ -2x } } frac { d }{ dx } left( { e }^{ -x } right)
=-cosleft( { tan }^{ -1 }{ e }^{ -x } right) frac { 1 }{ 1+{ e }^{ -2x } } .left( { e }^{ -x } right)

Ex 5.4 Class 12 Maths Question 5.
log(cosquad { e }^{ x })=y
Solution:
frac { dy }{ dx } =frac { 1 }{ cosquad { e }^{ x } } left( -sin{ e }^{ x } right) .{ e }^{ x }quad =-tanleft( { e }^{ x } right)

Ex 5.4 Class 12 Maths Question 6.
{ e }^{ x }+{ e }^{ { x }^{ 2 } }++{ e }^{ { x }^{ 5 } }=y(say)
Solution:
letquad u={ e }^{ { x }^{ n } },putquad { x }^{ n }=t,u={ e }^{ t },t={ x }^{ n }
{ e }^{ x }+{ e }^{ { x }^{ 2 } }++{ e }^{ { x }^{ 5 } }=y(say)
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability 6

Ex 5.4 Class 12 Maths Question 7.
sqrt { { e }^{ sqrt { x } } } ,x>0″><br><strong>Solution:</strong><br>y = <img src=
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability 7

Ex 5.4 Class 12 Maths Question 8.
log(log x),x>1
Solution:
y = log(log x),
put y = log t, t = log x,
differentiating
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability 8

Ex 5.4 Class 12 Maths Question 9.
frac { cosx }{ logx } =y(say),x>0 “><br><strong>Solution:</strong><br>let <img src=
tiwari academy class 12 maths Chapter 5 Continuity and Differentiability 9

Ex 5.4 Class 12 Maths Question 10.
cos(log x+ex),x>0
Solution:
y = cos(log x+ex),x>0
put y = cos t,t = log x+ex
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability 10

All Chapter NCERT Solutions For Class12 Maths

—————————————————————————–

All Subject NCERT Solutions For Class12

*************************************************

Remark:

I think you got complete solutions for this chapter. If You have any queries regarding this chapter, please comment on the below section our subject teacher will answer you. We tried our best to give complete solutions so you got good marks in your exam.

If these solutions have helped you, you can also share Careerkundali.in to your friends.

Best of Luck!!

Leave a Comment

Your email address will not be published. Required fields are marked *