a. $y'=\frac{-10sin(\frac{\pi}{6}-5x)}{cos^2(\frac{\pi}{6}-5x)}=\frac{-10tan(\frac{\pi}{6}-5x)}{cos(\frac{\pi}{6}-5x)}$
b. $y'=\frac{2x^2.cosx^2-sinx^2}{x^2}$
c. $y'=\frac{1}{cos^2x}+\frac{1}{sin^2x}=\frac{1}{sin^2x.cos^2x}=\frac{4}{sin^2x}$
d. $y'=\frac{-(\sqrt{1+x^2})'}{sin^2\sqrt{1+x^2}}=\frac{-x}{\sqrt{1+x^2}.sin^2\sqrt{1+x^2}}$