How do I find the derivative of # f(x) = x tan^-1 - ln sqrt(1+x^2)#?

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Answer 1 · 2018-04-25T10:48:10

# tan^-1x#.

#f(x)=xtan^-1x-lnsqrt(1+x^2)=xtan^-1x-ln(1+x^2)^(1/2)#.

#:. f(x)=xtan^-1x-1/2ln(1+x^2)#.

Using the usual rules of diffn., we get,

#f'(x)=x*d/dx{tan^-1x}+tan^-1x*d/dx{x}#

#-1/2*d/dx{ln(1+x^2)}#,

#=x*1/(1+x^2)+tan^-1x-1/2*1/(1+x^2)*d/dx{1+x^2}#,

#=x/(1+x^2)+tan^-1x-1/cancel2*1/(1+x^2)*cancel(2)x#,

#=cancel(x/(1+x^2))+tan^-1x-cancel(x/(1+x^2))#.

# rArr f'(x)=tan^-1x#.

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