Question

Найти производную функции:

Answer 1

$f^{'}(x)=(\sqrt{1-2x}-\cos{x}+\sin{x})^{'}=\\ =\frac{1}{2\sqrt{1-2x}}*(-2)-(-\sin{x})+\cos{x}=-\frac{1}{\sqrt{1-2x}}+\sin{x}+cos{x}$
$f^{'}(x)=(x-1)^{'} \arctan{x}+(x-1)(\arctan{x})^{'}=\\ =\arctan{x}+(x-1)*\frac{1}{1+x^2}$
$y{'}=(2\ln{x^2}+3\sin{2x})^{'}=2^{'}*\ln{x^2}+2*(\ln{x^2})^{'}+3^{'}*\sin{2x}+\\ +3*(\sin{2x})^{'}=2*\frac{1}{x^2}*2x+3*\cos{2x}*2=\frac{4}{x}+6\cos{2x}$