Question

If
$\sqrt{x} + \sqrt{y } = \sqrt{10} \: \: show \: that \: dy \div dx + \sqrt{y \div x}$=0(on the chapter continuation and differentiation in that second order derivatives of 12th)
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Answer 1

Step-by-step explanation:

We have,

$\sqrt{x} + \sqrt{y} = \sqrt{10}$

Differentiating both sides,

$\implies \frac{1}{2 \sqrt{x} } + \frac{1}{2 \sqrt{y} } . \frac{dy}{dx} = 0$

$\implies \frac{dy}{dx} = - \frac{2 \sqrt{y} }{2 \sqrt{x} }$

$\implies \frac{dy}{dx} = - \sqrt{ \frac{y}{x} }$

$\implies \frac{dy}{dx} + \sqrt{ \frac{y}{x} } = 0$