If \[y={{x}^{2}}+\frac{1}{{{x}^{2}}+\frac{1}{{{x}^{2}}+\frac{1}{{{x}^{2}}+......\infty }}},\]then \[\frac{dy}{dx}=\]

• A. \[\frac{2xy}{2y-{{x}^{2}}}\]
• B. \[\frac{xy}{y+{{x}^{2}}}\]
• C. \[\frac{xy}{y-{{x}^{2}}}\]
• D. \[\frac{2xy}{2+\frac{{{x}^{2}}}{y}}\]