What's the derivative of $f(x) = arctan[x/(sqrt(5-x^2))]$ ?

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Answer 1 · 2017-02-18T09:17:32

$1/sqrt(5-x^2)$

Let $x = sqrt5sint$ . Then,

$f =arctan(tant)=t=arcsin(1/sqrt5x)$ . So,

$f'=1/sqrt(1-x^2/5)(x/sqrt5)'$

$=sqrt5/(sqrt(5-x^2))(1/sqrt5)=1/sqrt(5-x^2)$

What's the derivative of f(x) = arctan[x/(sqrt(5-x^2))] f(x) = arctan[x/(sqrt(5-x^2))]?