derivative of ln(x^2-4x+5)

解

\frac{d}{d x} (ln (x^{2} - 4 x + 5))

\frac{2 x - 4}{x ^{2} - 4 x + 5}

解答ステップ

\frac{d}{d x} (ln (x^{2} - 4 x + 5))

連鎖法則を適用:

\frac{1}{x ^{2} - 4 x + 5} \frac{d}{d x} (x^{2} - 4 x + 5)

= \frac{1}{x ^{2} - 4 x + 5} \frac{d}{d x} (x^{2} - 4 x + 5)

\frac{d}{d x} (x^{2} - 4 x + 5) = 2 x - 4

= \frac{1}{x ^{2} - 4 x + 5} (2 x - 4)

簡素化

\frac{1}{x ^{2} - 4 x + 5} (2 x - 4) : \frac{2 x - 4}{x ^{2} - 4 x + 5}

= \frac{2 x - 4}{x ^{2} - 4 x + 5}