Prove $(V\cdot\nabla)X = V$ using index notation, where $V$ and $X$ are vectors.
I tried doing $$\Big[(V\cdot\nabla)X\Big]_i = V_i \frac{\partial}{\partial X^i}X_j $$ but I don't know what can I do next.
2026-03-26 14:33:22.1774535602
Prove $(V\cdot\nabla)X = V$ using index notation
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$$V_i\frac{\partial}{\partial X_i}X_j=V_i\delta_{ij}$$ does this help?