\(Stel\;\;y=\sqrt{x+\sqrt{x+\sqrt{x+...}}}\)
dan is   y² = x + y   (!)
en   y² − y + x = 0
Discriminant is   1 + 4x.
\(\large y=\frac{1+\sqrt{1+4x}}{2}\)   ( y ≥ 0)
\(\large D_x\;y=\frac12.\frac {1.4} {2.\sqrt{1+4x}}=\frac{1}{\sqrt{1+4x}} \)