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

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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