(log_{10}(1+x))^'

解

(lo g_{10} (1 + x))^{^{'}}

\frac{1}{ln ( 10 ) ( 1 + x )}

解答ステップ

(lo g_{10} (1 + x))^{'}

対数の規則を適用する:

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

= (\frac{ln ( 1 + x )}{ln ( 10 )})^{^{'}}

定数を除去:

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

= \frac{1}{ln ( 10 )} (ln (1 + x))^{^{'}}

連鎖法則を適用:

\frac{1}{1 + x} (1 + x)^{'}

= \frac{1}{1 + x} (1 + x)^{'}

(1 + x)^{'} = 1

= \frac{1}{ln ( 10 )} \cdot \frac{1}{1 + x} \cdot 1

簡素化

\frac{1}{ln ( 10 )} \cdot \frac{1}{1 + x} \cdot 1 : \frac{1}{ln ( 10 ) ( 1 + x )}

= \frac{1}{ln ( 10 ) ( 1 + x )}