Math Doubts

Derivatives of Logarithmic functions

$(1) \,\,\,$ $\dfrac{d}{dx}{\, \log_{e}{f{(x)}}}$ $\,=\,$ $\dfrac{1}{f{(x)}} \dfrac{d}{dx}{\, f{(x)}}$

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$(2) \,\,\,$ $\dfrac{d}{dx}{\, \log_{a}{f{(x)}}}$ $\,=\,$ $\dfrac{1}{f{(x)} \log_{e}{a}} \dfrac{d}{dx}{\, f{(x)}}$

$(1) \,\,\,$ $\dfrac{d}{dx}{\, \log_{e}{x}}$ $\,=\,$ $\dfrac{1}{x}$

$(2) \,\,\,$ $\dfrac{d}{dx}{\, \log_{a}{x}}$ $\,=\,$ $\dfrac{1}{x \log_{e}{a}}$