Question $2$: $22$ Marks

Differentiate the following $to$ the appropriate independent variable and simplify where possible:

$(2\mathrm{.}1)y=\frac{1}{x}-\sqrt[\phantom{2}]{cosx}$

$(2\mathrm{.}2)y=(x^3+2)(x^2-2x+1)$

$(2\mathrm{.}3)y=\frac{\sqrt[\phantom{2}]{1+ta{n}^{2}x}}{se{c}^{2}x}$

$(2\mathrm{.}4)y=ln|e^x(\frac{x-2}{x+3}{)}^{\frac{3}{4}}|$