Question

Номер 7.91 найти производную ​

Answer 1

$1. f(x)'=2sin(x)cos(x)+sin(x)=sin(2x)+sin(x)=2sin(\frac{3x}{2} )cos(\frac{x}{2} )\\2. f(x)' =2sin(x)cos(x)-\frac{1}{2} \\3. f(x)'=cos(x)+\frac{1}{cos^2(x)} \\4. f(x)'=1+\frac{1}{1+x^2} \\5. f(x)'=\frac{\sqrt{2} }{2} -sin(x)\\6. f(x)'=\frac{-sin(x)(2+sin(x))-cos(x)^2}{(2+sin(x))^2} =\frac{-2sin(x)-sin^2(x)-cos^2(x)}{(2+sin(x))^2} =\frac{-2sin(x)-1}{(2+sin(x))^2}$