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

Question

10910 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-04T02:41:34

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

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

Apply standard derivative and chain rule.

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

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

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

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

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