derivative of log_{10}((x-3^2))

解

\frac{d}{d x} (lo g_{10} ((x - 3)^{2}))

\frac{2}{ln ( 10 ) ( x - 3 )}

解答ステップ

\frac{d}{d x} (lo g_{10} ((x - 3)^{2}))

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 - 3 ) ^{2} )}{ln ( 10 )}

定数を除去:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln ((x - 3)^{2}))

連鎖法則を適用:

\frac{1}{( x - 3 ) ^{2}} \frac{d}{d x} ((x - 3)^{2})

= \frac{1}{( x - 3 ) ^{2}} \frac{d}{d x} ((x - 3)^{2})

\frac{d}{d x} ((x - 3)^{2}) = 2 (x - 3)

= \frac{1}{ln ( 10 )} \cdot \frac{1}{( x - 3 ) ^{2}} \cdot 2 (x - 3)

簡素化

\frac{1}{ln ( 10 )} \cdot \frac{1}{( x - 3 ) ^{2}} \cdot 2 (x - 3) : \frac{2}{ln ( 10 ) ( x - 3 )}

= \frac{2}{ln ( 10 ) ( x - 3 )}