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

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (2 x^{3} - x^{2}) = 6 x^{2} - 2 x

= \frac{1}{2 x ^{3} - x ^{2}} (6 x^{2} - 2 x)

簡素化

\frac{1}{2 x ^{3} - x ^{2}} (6 x^{2} - 2 x) : \frac{2 ( 3 x - 1 )}{x ( 2 x - 1 )}

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