derivative of (ln(x^3)/(ln(x^2)))

解

\frac{d}{d x} (\frac{ln ( x ^{3} )}{ln ( x ^{2} )})

0

解答ステップ

\frac{d}{d x} (\frac{ln ( x ^{3} )}{ln ( x ^{2} )})

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 ^{3} ) ) ln ( x ^{2} ) - \frac{d}{d x} ( ln ( x ^{2} ) ) ln ( x ^{3} )}{( ln ( x ^{2} ) ) ^{2}}

\frac{d}{d x} (ln (x^{3})) = \frac{3}{x}

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

= \frac{\frac{3}{x} ln ( x ^{2} ) - \frac{2}{x} ln ( x ^{3} )}{( ln ( x ^{2} ) ) ^{2}}

簡素化

\frac{\frac{3}{x} ln ( x ^{2} ) - \frac{2}{x} ln ( x ^{3} )}{ln ^{2} ( x ^{2} )} : 0

= 0