\lim _{x \rightarrow 2} \frac{d}{d x}\left(\frac{\sin {2}\left(\frac{1}{x}+e{\left.x^{2} \sqrt[5]{x^{3}-1}\right)}-\sin \left(e{\sqrt{x}}\right)\right.}{1+\frac{x+1}{\frac{x{3}}{2+x{4}}}}\right){\ln \left(\frac{x{x{3}}+x{\sqrt{x}}}{e{\cos x}}\right)}
]