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人気のある微分積分 >

derivative log_{2}(log_{2}(x))

解

導関数

lo g_{2} (lo g_{2} (x))

解

\frac{1}{ln ^{2} ( 2 ) x lo g _{2} ( x )}

解答ステップ

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

定数を除去:

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

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

連鎖法則を適用:

\frac{1}{lo g _{2} ( x )} \frac{d}{d x} (lo g_{2} (x))

= \frac{1}{lo g _{2} ( x )} \frac{d}{d x} (lo g_{2} (x))

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

= \frac{1}{ln ( 2 )} \cdot \frac{1}{lo g _{2} ( x )} \cdot \frac{1}{x ln ( 2 )}

簡素化

\frac{1}{ln ( 2 )} \cdot \frac{1}{lo g _{2} ( x )} \cdot \frac{1}{x ln ( 2 )} : \frac{1}{ln ^{2} ( 2 ) x lo g _{2} ( x )}

= \frac{1}{ln ^{2} ( 2 ) x lo g _{2} ( x )}

グラフ

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