derivative of ln(x^2-7x+1)

解

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

\frac{2 x - 7}{x ^{2} - 7 x + 1}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

= \frac{2 x - 7}{x ^{2} - 7 x + 1}