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)
-> Implicit differentiation with respect to x...
Left side :
Right side :
By the chain rule, this is :
- (we'll assume x>0...)
So we finally have :
(this implies that - this will be useful for later)
Differentiate implicitely, again with respect to x.
(I don't know if there is an easier way to do it though...)