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How do you differentiate #f(x)=x(arctanx)^2#?

1 Answer

Mar 5, 2015

I would use the Product Rule for the product between #x# and #arctan# and the Chain Rule for the #arctan^2(x)#.

So you get:

#f'(x)=1*arctan^2(x)+x*2arctan(x)*(1/(1+x^2))=#
#=arctan(x)[arctan(x)+(2x)/(1+x^2)]#

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