if d^2y/dx^2= x/x^2 +1, find d^4y/dx^4

Answer 1

d"=x/u where u = x^2+1

d"'= 1/u - x/u^2 * du/dx

d""= 1/u^2 -1/u^2 du/dx +2x/u^3 (du/dx)^2- x/u^2 d"u/dx"

so now it is the algebra

du/dx= 2x
d"u/dx"= 2

go for it. check my work.