derivative of ln(1-5x^2+x^3)

解

\frac{d}{d x} (ln (1 - 5 x^{2} + x^{3}))

\frac{3 x ^{2} - 10 x}{1 - 5 x ^{2} + x ^{3}}

解答ステップ

\frac{d}{d x} (ln (1 - 5 x^{2} + x^{3}))

連鎖法則を適用:

\frac{1}{1 - 5 x ^{2} + x ^{3}} \frac{d}{d x} (1 - 5 x^{2} + x^{3})

= \frac{1}{1 - 5 x ^{2} + x ^{3}} \frac{d}{d x} (1 - 5 x^{2} + x^{3})

\frac{d}{d x} (1 - 5 x^{2} + x^{3}) = 3 x^{2} - 10 x

= \frac{1}{1 - 5 x ^{2} + x ^{3}} (3 x^{2} - 10 x)

簡素化

\frac{1}{1 - 5 x ^{2} + x ^{3}} (3 x^{2} - 10 x) : \frac{3 x ^{2} - 10 x}{1 - 5 x ^{2} + x ^{3}}

= \frac{3 x ^{2} - 10 x}{1 - 5 x ^{2} + x ^{3}}