Question

y=√cos x +1

Найдите производную функции .

Answer 1

$1)\; \; y=\sqrt{cosx+1}\\\\\star \; \; (\sqrt{u})'=\frac{1}{2\sqrt{u}}\cdot u'\; ,\; \; u=cosx+1\; \star \\\\y'=\frac{1}{2\sqrt{cosx+1}}\cdot (cosx+1)'=\frac{1}{2\sqrt{cosx+1}}\cdot (-sinx+0)=-\frac{sinx}{2\sqrt{cosx+1}}\\\\\\2)\; \; y=\sqrt{cosx}+1\\\\y'=\frac{1}{2\sqrt{cosx}}\cdot (cosx)'+1'=\frac{1}{2\sqrt{cosx}}\cdot (-sinx)+0=-\frac{sinx}{2\sqrt{cosx}}$