derivative of (ln(x^5)/(ln(x^4)))

解

\frac{d}{d x} (\frac{ln ( x ^{5} )}{ln ( x ^{4} )})

0

解答ステップ

\frac{d}{d x} (\frac{ln ( x ^{5} )}{ln ( x ^{4} )})

商の法則を適用:

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

= \frac{\frac{d}{d x} ( ln ( x ^{5} ) ) ln ( x ^{4} ) - \frac{d}{d x} ( ln ( x ^{4} ) ) ln ( x ^{5} )}{( ln ( x ^{4} ) ) ^{2}}

\frac{d}{d x} (ln (x^{5})) = \frac{5}{x}

\frac{d}{d x} (ln (x^{4})) = \frac{4}{x}

= \frac{\frac{5}{x} ln ( x ^{4} ) - \frac{4}{x} ln ( x ^{5} )}{( ln ( x ^{4} ) ) ^{2}}

簡素化

\frac{\frac{5}{x} ln ( x ^{4} ) - \frac{4}{x} ln ( x ^{5} )}{ln ^{2} ( x ^{4} )} : 0

= 0