Найти производные первого порядка данных функций , используя правила вычисления...

Решите задачу:

$1)\; \; y=arccosx^2+arcctgx^2\\\\y'= -\frac{2x}{\sqrt{1-x^4}} +\frac{2x}{1+x^4} \\\\2)\; \; xy=cos(x-y)\\\\x'y+xy'=-sin(x-y)\cdot (x-y)'\\\\y+xy'=-sin(x-y)\cdot (1-y')\\\\y+xy'=-sin(x-y)+y'\cdot sin(x-y)\\\\xy'-y'\cdot sin(x-y)=-y-sin(x-y)\\\\y'\cdot \Big (x-sin(x-y)\Big )=-y-sin(x-y)\\\\y'= \frac{y+sin(x-y)}{sin(x-y)-x}$

$3)\; \; y=log_2(x^2+1)\\\\y'= \frac{1}{x^2+1} \cdot 2x= \frac{2x}{x^2+1} \\\\4)\; \; y=\frac{\sqrt{1-x^2}}{\sqrt{1+2^{x}}}=\sqrt{\frac{1-x^2}{1+2^{x}}}\\\\y'=\frac{1}{2}\cdot \sqrt{\frac{1+2^{x}}{1-x^2}}\cdot \frac{-2x(1+2^{x})-(1-x^2)\cdot 2^{x}\cdot ln2}{(1+2^{x})^2}$