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人気のある微分積分 >

derivative f(x)=log_{2}(3x)

解

導関数

f (x) = lo g_{2} (3 x)

解

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

解答ステップ

\frac{d}{d x} (lo g_{2} (3 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 ( 3 x )}{ln ( 2 )})

定数を除去:

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

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

連鎖法則を適用:

\frac{1}{3 x} \frac{d}{d x} (3 x)

= \frac{1}{3 x} \frac{d}{d x} (3 x)

\frac{d}{d x} (3 x) = 3

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

簡素化

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

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

グラフ

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