**3.6: Derivatives of Logarithmic Functions - Mathematics LibreTexts**
https://math.libretexts.org/Bookshelves/Calculus/Map%3A_Calculus__Early_Transcendentals_(Stewart)/03%3A_Differentiation_Rules/3.06%3A_Derivatives_of_Logarithmic_Functions

WebNov 10, 2020 · What about the functions \( a^x\) and \( \log_a x\)? We know that the derivative of \( a^x\) is some constant times \( a^x\) itself, but what constant? Remember that "the logarithm is the exponent'' and you will see that \( a=e^{\ln a}\). Then \(a^x = (e^{\ln a})^x = e^{x\ln a},\) and we can compute the derivative using the chain rule:

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