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Answer 1 · 2018-02-19T18:02:18

$\frac{d y}{d x} = \frac{1}{2 \sqrt{x (1 - x)}}$ $dy/dx=1/(2sqrt(x(1-x)$

$Let y = {sin}^{- 1} (\sqrt{x})$ $"Let"y=sin^-1(sqrtx)$

$\frac{d y}{d x} = ?$ $dy/dx=?$

$u = \sqrt{x}$ $u=sqrtx$

$u^{2} = x$ $u^2=x$

$\frac{d u}{d x} = \frac{1}{2 \sqrt{x}}$ $(du)/dx=1/(2sqrtx)$

$y = {sin}^{- 1} u$ $y=sin^-1u$

$\frac{d y}{d u} = \frac{1}{\sqrt{1 - u^{2}}}$ $(dy)/(du)=1/sqrt(1-u^2)$

$\frac{d y}{d u} = \frac{1}{\sqrt{1 - x}}$ $(dy)/(du)=1/sqrt(1-x)$

$\frac{d y}{d x} = \frac{d y}{d u} \frac{d u}{d x}$ $dy/dx=dy/(du)(du)/dx$

$\frac{d y}{d x} = \frac{1}{\sqrt{1 - x}} \times \frac{1}{2 \sqrt{x}} = \frac{1}{2 \sqrt{x (1 - x)}}$ $dy/dx=1/sqrt(1-x)xx1/(2sqrtx)=1/(2sqrt(x(1-x)$

$\frac{d y}{d x} = \frac{1}{2 \sqrt{x (1 - x)}}$ $dy/dx=1/(2sqrt(x(1-x)$