How do you differentiate #xarctan(x)#?

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Answer 1 · 2018-05-09T14:31:05

#=>(dy)/(dx)=tan^-1x+x/(1+x^2)#

Here,

#y=x*tan^-1x#

#"Using "color(blue)"Product Rule:"#, diff.w.r.t. #x#

#color(blue)(d/(dx)(u*v)=ud/(dx)(v)+vd/(dx)(u)#

Let, #u=x and v=tan^-1x#

#:.(dy)/(dx)=x*d/(dx)(tan^-1x)+tan^-1x*d/(dx)(x)#

#=>(dy)/(dx)=x(1/(1+x^2))+tan^-1x(1)#

#=>(dy)/(dx)=tan^-1x+x/(1+x^2)#