Let $X, Y \in M_n(\mathbb{C})$. Is the following true?
$$\frac{d}{dt}(X+tY)^m = m(X+tY)^{m-1}Y$$
I believe it's true if $X$ and $Y$ commute, but what about if they don't? How do I calculate the derivative in such a case?
2026-04-06 23:03:03.1775516583
Derivative of $t \mapsto (X+tY)^m$
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