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

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Answer 1 · 2017-11-18T15:18:21

Derivative is $(2arcsinx)/sqrt(1-x^2)$

Let us first workout derivative of $arcsinx$ . Let $y=arcsinx$ i.e. $siny=x$ and hence differentiating

$cosy*(dy)/(dx)=1$ or $(dy)/(dx)=1/cosy=1/sqrt(1-sin^2y)=1/sqrt(1-x^2)$

Hence $d/(dx)(arcsinx)^2=2arcsinx xx d/(dx)arcsinx$

= $(2arcsinx)/sqrt(1-x^2)$

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