Question: Let f : ( / 2 , / 2 ) R be defined by f ( x ) = tan x . Let u :

Let f : (/2, /2) R be defined by
f (x)= tan x .
Let u : R (/2, /2) denote its inverse, so
that, for every x in R,
x =(f u)(x).
Use implicit differentiation to deduce that, for every x in R,
u(x)=1/(1+ x2)

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