2.2.23 Derivatives and differentials

Problem: Find the derivatives of the functions: a) \( y=3 \sqrt[3]{\frac{x+1}{(x-1)^{2}}} \), b) \( y=x-3 \ln \left[\left(1+e^{\frac{x}{6}}\right) \sqrt{1+e^{\frac{x}{3}}}\right. \), c) \( y=\frac{1}{2} \sqrt{\frac{1}{x^{2}}-1}-\frac{\arccos x}{2 x^{2}} \), d) \( y=\ln \left(\arccos \frac{1}{\sqrt{x}}\right) \), e) \( y=\frac{6^{x}(\sin 4 x \ln 6-4 \cos 4 x)}{16+\ln ^{2} 6} \), f) \( x=\left(1+\cos ^{2} t\right)^{2}, y=\frac{\cos t}{\sin ^{2} t} \).