derivative of ln(6x^4-9x-3)

解

\frac{d}{d x} (ln (6 x^{4} - 9 x - 3))

\frac{8 x ^{3} - 3}{2 x ^{4} - 3 x - 1}

解答ステップ

\frac{d}{d x} (ln (6 x^{4} - 9 x - 3))

連鎖法則を適用:

\frac{1}{6 x ^{4} - 9 x - 3} \frac{d}{d x} (6 x^{4} - 9 x - 3)

= \frac{1}{6 x ^{4} - 9 x - 3} \frac{d}{d x} (6 x^{4} - 9 x - 3)

\frac{d}{d x} (6 x^{4} - 9 x - 3) = 24 x^{3} - 9

= \frac{1}{6 x ^{4} - 9 x - 3} (24 x^{3} - 9)

簡素化

\frac{1}{6 x ^{4} - 9 x - 3} (24 x^{3} - 9) : \frac{8 x ^{3} - 3}{2 x ^{4} - 3 x - 1}

= \frac{8 x ^{3} - 3}{2 x ^{4} - 3 x - 1}