derivative of ln(x^2-16x)

解

\frac{d}{d x} (ln (x^{2} - 16 x))

\frac{2 x - 16}{x ^{2} - 16 x}

解答ステップ

\frac{d}{d x} (ln (x^{2} - 16 x))

連鎖法則を適用:

\frac{1}{x ^{2} - 16 x} \frac{d}{d x} (x^{2} - 16 x)

= \frac{1}{x ^{2} - 16 x} \frac{d}{d x} (x^{2} - 16 x)

\frac{d}{d x} (x^{2} - 16 x) = 2 x - 16

= \frac{1}{x ^{2} - 16 x} (2 x - 16)

簡素化

\frac{1}{x ^{2} - 16 x} (2 x - 16) : \frac{2 x - 16}{x ^{2} - 16 x}

= \frac{2 x - 16}{x ^{2} - 16 x}