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Any Calculus researchers interested in disproving this theorem with a simple base and function?

Orion1 change of base theorem:

[tex]\frac{d}{dx} (\log_v u) = \frac{1}{u \ln(v)} \frac{du}{dx} - \frac{\ln(u)}{v \ln^2 (v)} \frac{dv}{dx}[/tex]

Is this theorem correct?

Does this theorem accept functions in the base?

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# First Derivative CoB Theorem

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