Question

Найдите производные

$y=(x+1)^{2} \sqrt{x-1}\\y=\frac{1}{2} cos^{2}\frac{x}{2} \\y=sin* e^{x} \\y=x^{2} *e^{-2x}$

Answer 1

$y'=\left((x+1)^2\sqrt{x-1}\right)_x'=2(x+1)\sqrt{x-1}+\frac{(x+1)^2}{2\sqrt{x-1}}$

$y'=\left( 0.5cos^2(x/2)\right)_x'=0.5*2*cos(x/2)*(-sin(x/2))*0.5=-(1/2)*cos(x/2)*sin(x/2)$

$y'=(sin(x)e^x)_x'=cos(x)e^x+sin(x)e^x=e^x(sin(x)+cos(x))$

$y'=(x^2e^{-2x})_x'=2xe^{-2x}+x^2e^{-2x}*(-2)=2xe^{-2x}(1-x)$