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Differentiation — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDifferentiation1 Mark
Question
Diffrentiate the following w. r. t. x.

$\tan ^{-1}(\sqrt{x})$

✓

Answer

Let $y =\tan ^{-1}(\sqrt{x})$

Differentiating w.r.t. x, we get

$\begin{aligned} \frac{d y}{d x} & =\frac{d}{d x}\left[\tan ^{-1}(\sqrt{x})\right] \\ & =\frac{1}{1+(\sqrt{x})^2} \cdot \frac{d}{d x}(\sqrt{x}) \\ & =\frac{1}{1+x} \times \frac{1}{2 \sqrt{x}}\end{aligned}$

$=\frac{1}{2 \sqrt{x}(1+x)}$

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