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

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Answer 1 · 2018-03-29T23:54:24

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

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

We can find the derivative $f'(x)$ using the chain rule.

$f'(x)=3(arctanx)^2*color(red)(d/dxarctanx)$

The derivative of $arctanx$ can be found on most tables that list derivatives of trigonometric functions.

$d/dxarctanx=1/(1+x^2)$

$f'(x)=3(arctanx)^2*color(red)(1/(1+x^2))$

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

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