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Prove that (d)/(dx)(cot^(-1)x)=(-1)/((1+...

Prove that `(d)/(dx)(cot^(-1)x)=(-1)/((1+x^(2)))`, where `x in R`.

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Let `y=cot(-1)x`, where `x in R and y in [0,pi]`. Then,
`x=cot y`
`rArr(dx)/(dy)=-"cosec"^(2)y=-(1+cot^(2)y)=-(1+x^(2))`
`rArr(dy)/(dx)=(-1)/((1+x^(2))).` ltbr. Hence, `(d)/(dx)(cot^(-1)x)=(-1)/((1+x^(2))).`
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