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pls help me ,I couldnt solve these q1: if y=e x+e^x+e^x+...........∞ ,then dy/dx equals q2:if x=at 2 and y=2at then (xy*d 2 y/dx 2) is equal to thank u

pls help me ,I couldnt solve these


q1: if y=ex+e^x+e^x+...........∞,then dy/dx equals


q2:if x=at2 and y=2at then (xy*d2y/dx2)  is equal to


thank u

Grade:10

2 Answers

AKASH GOYAL AskiitiansExpert-IITD
419 Points
11 years ago

Dear Rishabh

I think there is some mistake in question 1

confirm the qustion and try to do it by taking log

question2

dy/dx= (dy/dt)/(dx/dt)

dy/dt=2a

dx/dt=2at

dy/dx=1/t

d2y/dx2= d/dx(dy/dx)

use chain rule

d2y/dx2= d/dt(dy/dx)*dt/dx

=d/dt(1/t)*1/2at

=-(1/t2)*1/2at

=-1/2at3

xyd2y/dx2=at2*2at*(-1/2at3)= -a

 

 All the best.                                                          

AKASH GOYAL

AskiitiansExpert-IIT Delhi

 

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vikas askiitian expert
509 Points
11 years ago

1)

y=ex+e^x+e^x+...........∞

Y =ex+y 

dy/dx = ex+y(1+dy/dx)

dy/dx = (ex+y/1-ex+y )


2)

x=at2 ...........1

y=2at    ..............2

x/y = t/2   .........3

put t in eq 2

y = 4ax/y

y2 = 4ax

now differentiating above eq

2ydy/dx = 4a         .............1

again differentiating

2[(dy/dx)2 +yd2y/dx2] = 0        

d2y/dx2 = -(dy/dx)2/y          ..........2

multiply above eq by xy

(d2y/dx2)xy = -x(dy/dx)2

                      =-x(2a/y)2                    (from eq 1)

approve if u like my ans


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