Question

Найдите производную функции у= 1+х/кв.корень(1-х)

Answer 1

$y=\frac{u}{v}\\y'=\frac{u'v-uv'}{v^2}\\\\y=\frac{1+x}{\sqrt{1-x}}\\y'=\frac{(1+x)'\cdot\sqrt{1-x}-(1+x)\cdot(\sqrt{1-x})'}{(\sqrt{1-x})^2}=\frac{\sqrt{1-x}-\frac{1+x}{2\sqrt{1-x}}\cdot(-1)}{1-x}=\frac{\frac{2-2x+1+x}{2\sqrt{1-x}}}{1-x}=\\=\frac{3-x}{2(1-x)\sqrt{1-x}}=\frac{3-x}{2(1-x)^{\frac32}}$