DN1.1: DIFFERENTIATION FROM FIRST PRINCIPLES
By the way, do equations need equals signs? Or is it equalities that need equals signs?
It doesn't affect the argument. Sadly I don't have enough reputation to comment, so I guess I will post an answer instead.
I hope its not inappropriate. In fact one definition is implicitly by:.
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Differentiation (Finding Derivatives)
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The answer can vary. Dec 6 '15 at Others define it as the inverse function of log, so that that's a proof by first principles.
However, isn't there a particular way in which the above limit could still be evaluated? Akiva Weinberger Akiva Weinberger Bernoulli's inequality is powerful. That other property follows from the laws of exponents. It's not too hard to define exponentiation with a positive real base and real exponent.
Introduction to differentiation
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Derivative from First Principles
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