Question

Найти производную y = (√a - √x)²

Answer 1

$y=\left(\sqrt{a} - \sqrt{x}\right)^2$

$y'=2\left(\sqrt{a} - \sqrt{x}\right)\cdot\left(\sqrt{a} - \sqrt{x}\right)'=2\left(\sqrt{a} - \sqrt{x}\right)\cdot\left(\0 - \dfrac{1}{2\sqrt{x} } \right)=$

$=- \dfrac{1}{\sqrt{x} }\left(\sqrt{a} - \sqrt{x}\right)= \dfrac{1}{\sqrt{x} }\left(\sqrt{x} - \sqrt{a}\right)=\boxed{1-\sqrt{\dfrac{a}x}}}$

Answer 2

Ответ:

$y=(\sqrt{a}-\sqrt{x})^2\ \ ,\ \ \ a=const\ \ ,\\\\\star \ \ (u^2)'=2u\cdot u'\ \ ,\ \ u=\sqrt{a}-\sqrt{x}\ \ \star \\\\y'=2(\sqrt{a}-\sqrt{x})\cdot (\sqrt{a}-\sqrt{x})'=2(\sqrt{a}-\sqrt{x})\cdot \dfrac{-1}{2\sqrt{x}}=\dfrac{\sqrt{x}-\sqrt{a}}{\sqrt{x}}=1-\dfrac{\sqrt{a}}{\sqrt{x}}\\\\y'=1-\sqrt{\dfrac{a}{x}}$