How do you differentiate arctan(1/x)?
1 Answer
Nov 9, 2016
d/dx arctan(1/x) = -1/(1+x^2)
Explanation:
We can write
:. 1/tany=x
:. coty=x ..... [1]
We can then differentiate implicitly:
-csc^2y dy/dx= 1
dy/dx= -1/csc^2y
Using the identity
dy/dx= -1/(1+cot^2y)
dy/dx= -1/(1+x^2) (from [1])