derivative y=ln(8x^2-7x+9)

解

導関数

y = ln (8 x^{2} - 7 x + 9)

\frac{16 x - 7}{8 x ^{2} - 7 x + 9}

解答ステップ

\frac{d}{d x} (ln (8 x^{2} - 7 x + 9))

連鎖法則を適用:

\frac{1}{8 x ^{2} - 7 x + 9} \frac{d}{d x} (8 x^{2} - 7 x + 9)

= \frac{1}{8 x ^{2} - 7 x + 9} \frac{d}{d x} (8 x^{2} - 7 x + 9)

\frac{d}{d x} (8 x^{2} - 7 x + 9) = 16 x - 7

= \frac{1}{8 x ^{2} - 7 x + 9} (16 x - 7)

簡素化

\frac{1}{8 x ^{2} - 7 x + 9} (16 x - 7) : \frac{16 x - 7}{8 x ^{2} - 7 x + 9}

= \frac{16 x - 7}{8 x ^{2} - 7 x + 9}