if x=ex/y
prove that
dy/dx = (x-y)/(xlogx)
I think the question is like this . x = ex/y .
Taking log on both sides , we get log x = x/y
Or ylogx = x
Now differentiating both sides w.r.t x , we get
yd/dx(logx) + logx d/dx(y) = d/dx(x) [ Product rule ]
or y/x + logx dy/dx = 1
Re arranging , logx dy/dx = 1- y/x = x-y/x
Again Re-arranging , we get dy/dx = (x – y)/xlogx
Hope that helps.
Taking log on both sides , we get log x = x/y
Or ylogx = x
Now differentiating both sides w.r.t x , we get
yd/dx(logx) + logx d/dx(y) = d/dx(x) [ Product rule ]
or y/x + logx dy/dx = 1
Re arranging , logx dy/dx = 1- y/x = x-y/x
Again Re-arranging , we get dy/dx = (x – y)/xlogx
Hope that helps.
