Question

if y=x^(1/2)+1/x^(1/2) the prove

2x dy/dx+y=2.x^(1/2)

Answer 1

$y= \sqrt{x} + \frac{1}{ \sqrt{x} } \\ \\ \frac{dy}{dx} = \frac{d}{dx}(\sqrt{x} + \frac{1}{ \sqrt{x} })\\ \\\frac{dy}{dx}= \frac{1}{2 \sqrt{x} } - \frac{1}{2x \sqrt{x} } \\ \\\frac{dy}{dx}= \frac{1}{2x} (\sqrt{x} - \frac{1}{ \sqrt{x} })\\ \\ 2x \frac{dy}{dx} =\sqrt{x} - \frac{1}{ \sqrt{x} }=2\sqrt{x} - \sqrt{x} - \frac{1}{ \sqrt{x} }\\ \\ 2x \frac{dy}{dx} =2\sqrt{x} -y\\ \\2x \frac{dy}{dx} +y=2 \sqrt{x}\ (proved)$