What is the derivative of ${arctan (x)}^{\frac{1}{2}}$ $arctan(x)^(1/2)$ ?

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Answer 1 · 2015-09-03T17:13:19

$f'(x)=(1)/(2sqrt(x)(1+x)$

$f(x)=arctan(x^(1/2))$

Using the chain rule:

$f'(x)=(1)/(1+x)xx1/2x^(-1/2)$

$f'(x)=(x^(-1/2))/(2(1+x))$

$f'(x)=(1)/(2sqrt(x)(1+x)$

What is the derivative of arctan(x)^(1/2)arctan(x)12arctan(x)^(1/2)?