derivative of (log_{3}(x)/(log_{7)(x)})

解答

\frac{d}{d x} (\frac{lo g _{3} ( x )}{lo g _{7} ( x )})

0

求解步骤

\frac{d}{d x} (\frac{lo g _{3} ( x )}{lo g _{7} ( x )})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( lo g _{3} ( x ) ) lo g _{7} ( x ) - \frac{d}{d x} ( lo g _{7} ( x ) ) lo g _{3} ( x )}{( lo g _{7} ( x ) ) ^{2}}

\frac{d}{d x} (lo g_{3} (x)) = \frac{1}{x ln ( 3 )}

\frac{d}{d x} (lo g_{7} (x)) = \frac{1}{x ln ( 7 )}

= \frac{\frac{1}{x l n ( 3 )} lo g _{7} ( x ) - \frac{1}{x l n ( 7 )} lo g _{3} ( x )}{( lo g _{7} ( x ) ) ^{2}}

化简

\frac{\frac{1}{x l n ( 3 )} lo g _{7} ( x ) - \frac{1}{x l n ( 7 )} lo g _{3} ( x )}{lo g _{7} ( x ) ^{2}} : 0

= 0

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