Question

Помогите решить 2 задания с производной

Answer 1

$1)\; \; f(x)=(3x^2+x)cos2x\\\\f'(x)=(6x+1)cos2x-2(3x^2+x)sin2x\\\\f'(0)+f'(-\frac{\pi}{2})=cos0+(-3\pi +1)cos(-\pi )-2(\frac{3\pi ^2}{4}-\frac{\pi }{2})sin(-\pi )=\\\\=1+(-3\pi +1)(-1)-0=3\pi$

$2)\; \; f(x)=|x+1|\\\\f'(x)= \left \{ {{1,\; esli\; x\ \textgreater \ -1}\atop {ne\; syshestvyet,\; esli\; x=-1 \atop {-1,\; esli\; x\ \textless \ 1}} \right.$