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Differentiation — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsDifferentiation3 Marks
Question
Differentiate the following w.r.t. x :$y=\frac{\sqrt{x}+5}{\sqrt{x}-5}$
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Answer

$y=\frac{\sqrt{x}+5}{\sqrt{x}-5}$
Differentiating w.r.t. $x$, we get
$\frac{ d y}{ d x}=\frac{ d }{ d x}\left(\frac{\sqrt{x}+5}{\sqrt{x}-5}\right)$
$=\frac{(\sqrt{x}-5) \frac{ d }{ d x}(\sqrt{x}+5)-(\sqrt{x}+5) \frac{ d }{ d x}(\sqrt{x}-5)}{(\sqrt{x}-5)^2}$
$=\frac{(\sqrt{x}-5)\left(\frac{1}{2 \sqrt{x}}\right)-(\sqrt{x}+5)\left(\frac{1}{2 \sqrt{x}}\right)}{(\sqrt{x}-5)^2}$
$=\frac{\frac{1}{2 \sqrt{x}}(\sqrt{x}-5-\sqrt{x}-5)}{(\sqrt{x}-5)^2}$
$=\frac{\frac{1}{2 \sqrt{x}}(-10)}{(\sqrt{x}-5)^2}=\frac{-5}{\sqrt{x}(\sqrt{x}-5)^2}$

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