Помогите вычислить производные: а)[latex]y=arctg(3+ln^2 \frac{2}{x} )

[latex]y=arctg(3+ln^2\, \frac{2}{x})\\\\(arctgu)'=\frac{1}{1+u^2}*u'\\\\(u^2)'=2uu'\\\\lnu=\frac{1}{u}*u'\\\\y'= \frac{1}{1+(3+ln^2\, \frac{2}{x})^2} \cdot 2\cdot ln\frac{2}{x}\cdot \frac{x}{2} \cdot (- \frac{2}{x^2} )= -\frac{2\cdot ln\frac{2}{x}}{x\cdot (1+(3+ln^2\, \frac{2}{x})^2)} [/latex] [latex]y=x^{-x}\\\\lny=ln(x^{-x})\\\\lny=-xlnx\\\\\frac{y'}{y}=-lnx-x\cdot \frac{1}{x}\\\\y'=y(-lnx-1)\\\\y'=x^{-x}(-lnx-1)[/latex]