derivative of ln(12-9x^2+2x^4)

解

\frac{d}{d x} (ln (12 - 9 x^{2} + 2 x^{4}))

\frac{8 x ^{3} - 18 x}{12 - 9 x ^{2} + 2 x ^{4}}

解答ステップ

\frac{d}{d x} (ln (12 - 9 x^{2} + 2 x^{4}))

連鎖法則を適用:

\frac{1}{12 - 9 x ^{2} + 2 x ^{4}} \frac{d}{d x} (12 - 9 x^{2} + 2 x^{4})

= \frac{1}{12 - 9 x ^{2} + 2 x ^{4}} \frac{d}{d x} (12 - 9 x^{2} + 2 x^{4})

\frac{d}{d x} (12 - 9 x^{2} + 2 x^{4}) = 8 x^{3} - 18 x

= \frac{1}{12 - 9 x ^{2} + 2 x ^{4}} (8 x^{3} - 18 x)

簡素化

\frac{1}{12 - 9 x ^{2} + 2 x ^{4}} (8 x^{3} - 18 x) : \frac{8 x ^{3} - 18 x}{12 - 9 x ^{2} + 2 x ^{4}}

= \frac{8 x ^{3} - 18 x}{12 - 9 x ^{2} + 2 x ^{4}}