derivative of ln(8x^2+7x+2)

解

\frac{d}{d x} (ln (8 x^{2} + 7 x + 2))

\frac{16 x + 7}{8 x ^{2} + 7 x + 2}

解答ステップ

\frac{d}{d x} (ln (8 x^{2} + 7 x + 2))

連鎖法則を適用:

\frac{1}{8 x ^{2} + 7 x + 2} \frac{d}{d x} (8 x^{2} + 7 x + 2)

= \frac{1}{8 x ^{2} + 7 x + 2} \frac{d}{d x} (8 x^{2} + 7 x + 2)

\frac{d}{d x} (8 x^{2} + 7 x + 2) = 16 x + 7

= \frac{1}{8 x ^{2} + 7 x + 2} (16 x + 7)

簡素化

\frac{1}{8 x ^{2} + 7 x + 2} (16 x + 7) : \frac{16 x + 7}{8 x ^{2} + 7 x + 2}

= \frac{16 x + 7}{8 x ^{2} + 7 x + 2}