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I'm studying Calculus, looking at the rules for deriving the function a^x. The first step is to change a^x to e^(x(lna)). From there, it's easy to use the chain rule to find the derivative.

Why can you do that first step though? I've tried googling around, and can't find an explanation.

Also, any tips on doing google searches for this kind of topic? I've tried pasting the equation into google; doing searches for "natural log" guides, "e" guides, and a browsed a few precalculus sites, but haven't found the answer I'm looking for.

Thanks!