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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