If u = e^(arcsin (y/u)), then prove that d^2y/dx^2 = 2(x^2 + y^2)/(x  y)^3 , where u = √(x^2 + y^2)
Hello,
This is equivalent to
> Implicit differentiation with respect to x...
Left side :
, where
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Right side :
:
By the chain rule, this is :
 (we'll assume x>0...)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So we finally have :
That is
(this implies that  this will be useful for later)
Differentiate implicitely, again with respect to x.
, where
>
(I don't know if there is an easier way to do it though...)