$\begin{align}  & y=\frac{\cos x}{{{x}^{2}}+\sin x} \\ & \text{Using quotient rule} \\ & \frac{dy}{dx}=\frac{({{x}^{2}}+\sin x)\tfrac{d}{dx}(\cos x)-\cos x\tfrac{d}{dx}({{x}^{2}}+\sin x)}{{{({{x}^{2}}+\sin x)}^{2}}} \\ & \frac{dy}{dx}=\frac{({{x}^{2}}+\sin x)(-\sin x)-\cos x(2x+\cos x)}{{{({{x}^{2}}+\sin x)}^{2}}} \\ & \frac{dy}{dx}=\frac{-{{x}^{2}}\sin x-{{\sin }^{2}}x-2x\cos x-{{\cos }^{2}}x}{{{({{x}^{2}}+\sin x)}^{2}}} \\ & \frac{dy}{dx}=\frac{-{{x}^{2}}\sin x-2x\cos x-({{\sin }^{2}}x+{{\cos }^{2}}x)}{{{({{x}^{2}}+\sin x)}^{2}}} \\ & \frac{dy}{dx}=\frac{-{{x}^{2}}\sin x-2x\cos x-1}{{{({{x}^{2}}+\sin x)}^{2}}} \\ & \frac{dy}{dx}=\frac{-(1+{{x}^{2}}\sin x+2x\cos x)}{{{({{x}^{2}}+\sin x)}^{2}}} \\\end{align}$