I want to prove $$f(x) - f(0) = \sum_{j=1}^nx_j\int_0^1 \frac{\partial}{\partial x_j} f((1-s)x) ds$$ for $f\in \mathcal{C}^\infty,$ and $x\in \mathbb{R}^n$. To be clear, $f: \mathbb{R}^n\to \mathbb{R}.$ I have tried various things but none have worked. Any thoughts?
2026-02-27 16:14:08.1772208848
Evaluating this integral/sum
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