Not simultaneously even & odd function.

Calculus Level 4

$f(x+y^{2n+1})=f(x)+f(y)^{2n+1} \ \text{and} \ n \in \mathbb{N}$

Let $$f(x)$$ be a real function not identically zero satisfying the above condition for any real numbers $$x,y$$. And provided with $$f'(0) \geq 0$$. Then find the value of $$f'(10)$$.

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