Question

Question #17d65

Answer 1

Let

`y=cot^{-1}x`.

By rewriting in terms of cotangent,

`Rightarrow coty=x`

by implicitly differentiating with respect to `x`,

`Rightarrow -csc^2y cdot {dy}/{dx}=1`

by dividing by `-cot^2y`,

`Rightarrow {dy}/{dx}=-1/{csc^2y}`

by the trig identity `csc^2theta=1+cot^2theta`,

`Rightarrow {dy}/{dx}=-1/{1+cot^2y}=-1/{1+x^2}`.

Hence,

`d/{dx}(cot^{-1}x)=-1/{1+x^2}`.

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I hope that this was helpful.