What's the derivative of (arctan x)^3?

1 Answer
Alan P.
Nov 9, 2017

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

Explanation:

Note:
color(white)("XXX")(d (arctan(x)))/(dx)=1/(1+x^2)
and
color(white)("XXX")(d(x^3))/(dx)=3x^2

Using the chain rule:
color(white)("XXX")(d(color(blue)((color(red)(arctan(x)))^3)))/(d(color(green)x))=(d(color(blue)((color(red)(arctan(x)))^3)))/(d(color(red)(arctan(x)))) * (d(color(red)(arctan(color(green)x))))/(dcolor(green)x)

color(white)("XXXXXXXXXXXXX")=3(arctan(x))^2 * 1/(1+x^2)

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