Second derivative for tan^-1x
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d^2y/dx^2=2x/(1+x^2)^2
Step-by-step explanation:
let y=tan^-1x
tany=x. --------------------------(1)
differentiation of respect with x :-
sec^2y dy/dx=1
now using trigonometry formula:-
(1+tan^2y)dy/dx=1
(1+x^2)dy/dx=1 [by eq.1]
dy/dx=1/(1+x^2)
now
again differentiate
d^2y/dx^2= d/dx(1/1+x^2)
d^2y/dx^2 =1/(1+x^2)^2 d/dx(1+x^2)
d^2y/dx^2=2x/(1+x^2)^2.
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