What's the derivative of $\sqrt{arctan (x)}$ $sqrt[arctan(x)]$ ?

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Answer 1 · 2016-11-24T18:48:08

$\frac{1}{2 (x^{2} + 1) \sqrt{arctan (x)}}$ $1/(2(x^2+1)sqrtarctan(x)$

This can be written as ${(arctan (x))}^{\frac{1}{2}}$ $(arctan(x))^(1/2)$ .

This is in the form $u^{\frac{1}{2}}$ $u^(1/2)$ . The chain rule with the power rule tells us that:

$d/dxu^(1/2)=1/2u^(-1/2)*u'=1/(2sqrtu)*u'$

So for $arctan(x)$ , whose derivative is $1/(x^2+1)$ , this becomes

$d/dxsqrtarctan(x)=1/(2sqrtarctan(x))*1/(x^2+1)$

What's the derivative of sqrt[arctan(x)]√arctan(x)sqrt[arctan(x)]?