What is the derivative of $(arctan x)^3$ ?

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Answer 1 · 2016-03-12T12:42:22

$f'(x)=(3arctan^2(x))/((x^2+1))$

$f(x)=arctan^3(x)$

Apply the chain rule:

$f'(x)=3arctan^2(x).(d(arctanx))/(dx)$

$=3xx1/((x^2+1)).arctan^2(x)$

$=(3arctan^2(x))/((x^2+1))$

What is the derivative of (arctan x)^3 (arctan x)^3 ?