Demostrate that:

Question

d/dx [tan^-1(x)]= 1/1+ x^2

-> using implicit differentiation

Answer 1

rewrite
y=atan(x) as
tan(y)=x
differentiate with respect to x:
sec²(y) dy/dx = 1
using 1+tan²(y)=sec²(y)
(1+tan²(y)) dy/dx = 1
dy/dx = 1/(1+tan²(y)
=1/(1+x²)

NOTE: The parentheses in the final answer are required.