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A function f : R rarr R satisfies th...

A function `f : R rarr R` satisfies the equation `f(x+y) = f(x). f(y)` for all `x y in R, f(x) ne 0`. Suppose that the function is differentiable at `x = 0` and `f'(0) = 2`, then prove that `f' = 2f(x)`.

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