derivative ln(6-x^2+2x^4)

解

導関数

ln (6 - x^{2} + 2 x^{4})

\frac{8 x ^{3} - 2 x}{6 - x ^{2} + 2 x ^{4}}

解答ステップ

\frac{d}{d x} (ln (6 - x^{2} + 2 x^{4}))

連鎖法則を適用:

\frac{1}{6 - x ^{2} + 2 x ^{4}} \frac{d}{d x} (6 - x^{2} + 2 x^{4})

= \frac{1}{6 - x ^{2} + 2 x ^{4}} \frac{d}{d x} (6 - x^{2} + 2 x^{4})

\frac{d}{d x} (6 - x^{2} + 2 x^{4}) = 8 x^{3} - 2 x

= \frac{1}{6 - x ^{2} + 2 x ^{4}} (8 x^{3} - 2 x)

簡素化

\frac{1}{6 - x ^{2} + 2 x ^{4}} (8 x^{3} - 2 x) : \frac{8 x ^{3} - 2 x}{6 - x ^{2} + 2 x ^{4}}

= \frac{8 x ^{3} - 2 x}{6 - x ^{2} + 2 x ^{4}}