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CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY2 Marks
Question
$\text{If y}=\text{sin}^{-1}(6\text{x}\sqrt{1-9\text{x}^2}), -\frac{1}{3\sqrt{2}}<\text{x}<\frac{1}{3\sqrt{2}},\text{then find}\frac{\text{dy}}{dx}$
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Answer

$\text{y}=\text{sin}^{-1}(6\text{x}\sqrt{1-9\text{x}^2}),-\frac{1}{3\sqrt2}<\text{x}<\frac{1}{3\sqrt2}$ $\text{put 3x}=\text{sin}\ \theta$ $\Rightarrow\theta=\text{sin}^{-1}3\text{x}$$\text{y}=\text{sin}^{-1}(\text{sin}\ 2\theta)$
$=2\theta$ $=2\ \text{sin}^{-1}3\text{x}$ $\therefore\ \frac{\text{dy}}{\text{dx}}=\frac{6}{\sqrt{1-9\text{x}^2}}$

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