derivative of log_{2}(2x+4)

解

\frac{d}{d x} (lo g_{2} (2 x + 4))

\frac{1}{ln ( 2 ) ( x + 2 )}

解答ステップ

\frac{d}{d x} (lo g_{2} (2 x + 4))

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 ( 2 x + 4 )}{ln ( 2 )})

定数を除去:

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

= \frac{1}{ln ( 2 )} \frac{d}{d x} (ln (2 x + 4))

連鎖法則を適用:

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

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

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

= \frac{1}{ln ( 2 )} \cdot \frac{1}{2 x + 4} \cdot 2

簡素化

\frac{1}{ln ( 2 )} \cdot \frac{1}{2 x + 4} \cdot 2 : \frac{1}{ln ( 2 ) ( x + 2 )}

= \frac{1}{ln ( 2 ) ( x + 2 )}