Question

How do you differentiate `arctan(x-1)`?

Answer 1

`y' = 1/( x^2 - 2x + 2)`

Explanation:

From `y = arctan(x-1)` you can say that `tan y = x-1`

And so by implicit differentiation `sec^2 y \ y' = 1`

Which means that:

`y' = 1/( sec^2 y) = 1/( tan^2 y + 1) = 1/( (x-1)^2 + 1 )= 1/( x^2 - 2x + 2)`