Lemma
DeepDifferentiation rules
Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §6.2 The Exponential e, #62 · Calculus · Differentiation rules

… is also proved by l'Hôpital's rule (at …):

is also proved by l'Hôpital's rule (at ):
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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §6.2 The Exponential e, #62

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