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If f(x)=xtan^(-1)x , find f^(prime)(1) u...

If `f(x)=xtan^(-1)x ,` find `f^(prime)(1)` using the first principle.

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Given `f(x)=x tan ^{-1} x`
Differentiate w.r.t.x
`f^{prime}(x)=tan ^{-1} x+x /(1+x^{2}) `
`f^{prime}(1)=tan ^{-1} 1+1 /(1+1^{2}) `
`=pi / 4+1 / 2`

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