Correction, you cannot find an explanation on the web EXCEPT for this site.Originally Posted bytttcomrader

Anyway, since it is inverse we have,

Now, take the derivative of both sides, (use chain rule),

.

Thus,

But,

Thus,

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Note, I assumed that the derivative of the arctangent exists. Which is true, because if a bijective function is differenciable then so is its inverse. But I did not bother with the proof here. It happens to be true.

Q.E.D.