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

解

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

\frac{3 x - 4}{x ( x - 2 )}

解答ステップ

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

連鎖法則を適用:

\frac{1}{x ^{3} - 2 x ^{2}} \frac{d}{d x} (x^{3} - 2 x^{2})

= \frac{1}{x ^{3} - 2 x ^{2}} \frac{d}{d x} (x^{3} - 2 x^{2})

\frac{d}{d x} (x^{3} - 2 x^{2}) = 3 x^{2} - 4 x

= \frac{1}{x ^{3} - 2 x ^{2}} (3 x^{2} - 4 x)

簡素化

\frac{1}{x ^{3} - 2 x ^{2}} (3 x^{2} - 4 x) : \frac{3 x - 4}{x ( x - 2 )}

= \frac{3 x - 4}{x ( x - 2 )}