How do I derive this $k$-th derivative: $\dfrac{d^k}{dt^k}e^{tx}=x^ke^{tx}?$
I believe that induction is to be used.
2026-04-25 19:25:56.1777145156
$k$-th derivative of an exponantial function
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Induction will work great, but I'll mention that you might be getting a bit confused or distracted by the variables they chose to use. I'm curious if you find
$$\dfrac{d^n}{dx^n}e^{ax}=a^n e^{ax}$$
a bit more obvious. Because it's the exact same thing as your question.