Find the derivative of / given by `f(x)=tan^(-1)x`assuming it exists.

Explanation

Given that `f(x)=tan^(-1)x`

let `y=tan^(-1)x`

`x=tany`

Apply `d/dx` on both the sides

`dx/dx=d/dx(tany)`

`sec^2ydy/dx=1`

`dy/dx=1/sec^2y`

`dy/dx=1/(1+tan^2y)`

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