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

							
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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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