Question

What is the derivative of `arctan(1/x)`?

Answer 1

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

Explanation:

`f(x) = arctan(1/x)`

Apply standard derivative and chain rule.

`f'(x) = 1/((1/x)^2+1) * d/dx (1/x)`

`= 1/(1/x^2+1) * (-1/x^2)`

`= x^2/(1+x^2) * (-1/x^2)`

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