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

2 Answers
Jun 11, 2015

The answer is (arctan(x+1))' = 1/((x+1)^2+1)

Explanation:

Let's start with an uncommon method,

We have theta = arctan(x+1)

tan(theta) = x+1

Derivate both side

theta'(tan^2(theta)+1) = 1

theta' = 1/(tan^2(theta)+1)

But tan(theta) = x+1

theta' = 1/((x+1)^2+1)

Jun 15, 2015

d/(dx)[arctanu] = 1/(1+u^2)((du)/(dx))

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

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

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