derivative of log_{2}(x^2-9x)

解

\frac{d}{d x} (lo g_{2} (x^{2} - 9 x))

\frac{2 x - 9}{ln ( 2 ) ( x ^{2} - 9 x )}

解答ステップ

\frac{d}{d x} (lo g_{2} (x^{2} - 9 x))

対数の規則を適用する:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( x ^{2} - 9 x )}{ln ( 2 )})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{ln ( 2 )} \frac{d}{d x} (ln (x^{2} - 9 x))

連鎖法則を適用:

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

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

\frac{d}{d x} (x^{2} - 9 x) = 2 x - 9

= \frac{1}{ln ( 2 )} \cdot \frac{1}{x ^{2} - 9 x} (2 x - 9)

簡素化

\frac{1}{ln ( 2 )} \cdot \frac{1}{x ^{2} - 9 x} (2 x - 9) : \frac{2 x - 9}{ln ( 2 ) ( x ^{2} - 9 x )}

= \frac{2 x - 9}{ln ( 2 ) ( x ^{2} - 9 x )}