calculus

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

-> using implicit differentiation

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  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.

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