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DIFFERENTIATION — Statistics STD 12 Commerce — Question

Gujarat BoardEnglish MediumSTD 12 CommerceStatisticsDIFFERENTIATION2 Marks
Question
Find $\frac{d y}{d x}, y=\sqrt{x^{2}+3}$.
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Answer

$ y=\sqrt{x^{2}+3} $
Taking $u=x^{2}+3, y=\sqrt{u}$
$ \therefore \frac{d u}{d x}=2 x \text { and } \frac{d y}{d u}=\frac{1}{2 \sqrt{u}} \text {. } $
Now, $\frac{d y}{d x}=\frac{d y}{d u} \times \frac{d u}{d x}$
$ =\left(\frac{1}{2 \sqrt{u}}\right)(2 x)$
$ =\frac{x}{\sqrt{u}} $
Putting value of $u$,
$ \frac{d y}{d x}=\frac{x}{\sqrt{x^{2}+3}} $

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