x^2 + y^2 = 4
y^2 = 4-x^2
y = sqrt( 4 - x^2)
1 -2x - x
dy/dx = ---------------------- d(4 - x^2 ) = --------------------- = ------------------
2* sqrt(4 - x^2) 2 sqrt( 4- x^2) sqrt( 4 - x^2)
d( - x)*sqrt(4 - x^2) - ( -x)d( sqrt(4 - x^2))
d^2y/d^2x = ----------------------------------------------------------
( sqrt(4 - x^2))^2
- sqrt( 4 - x^2) + x( -2x/2sqrt( 4 - x^2))
d^2y/d^2x = -----------------------------------------------
( 4 - x^2)
(- sqrt(4 - x^2) * sqrt( 4 - x^2) -x^2)/sqrt( 4 - x^2)
d^2y/d^2x = -------------------------------------------------------------
( 4 - x^2)
- ( 4 - x^2) - x^2 2( 2 + x^2)
d^2y/d^2x = ------------------------------- = - -------------------------
(4 - x^2) * sqrt( 4 - x^2) ( 4-x^2)sqrt(4 - x^2)