How do you find the derivative of $arcsin (x/2)$ ?

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Answer 1 · 2017-06-30T21:22:32

$d/dx(arcsin(x/2))=1/sqrt(4-x^2)$

The derivative of $arcsinu$ :

$d/dx(arcsinu)=(u')/sqrt(1-u^2)$

$therefored/dx(arcsin(x/2))=((x/2)')/sqrt(1-(x/2)^2)=(1/2)/sqrt(1-x^2/4)$
$=1/(2sqrt((4-x^2)/4))=1/sqrt(4-x^2)$

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