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

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Answer 1 · 2016-10-10T10:14:07

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

The rule for deriving the power of a function states that

$d/dx f^n(x) = n f^{n-1}(x) * f'(x)$

In your case, $f(x)=arctan(x)$ , and thus $f'(x) = 1/(1+x^2)$

Appling the rule with $n=3$ gives us

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

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