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The function f:R→R satisfies f(x^2 )....

The function `f:R→R` satisfies `f(x^2 ).f ′′ (x)=f ′ (x).f ′ (x^2 )` for all real x. Given that f(1)=1 and compute the value of `f ′ (1)+f ′′ (1)`.

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