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人気のある微分積分 >

derivative y=log_{5}(x)+log_{5}(x^4)

解

導関数

y = lo g_{5} (x) + lo g_{5} (x^{4})

解

\frac{5}{ln ( 5 ) x}

解答ステップ

\frac{d}{d x} (lo g_{5} (x) + lo g_{5} (x^{4}))

簡素化

lo g_{5} (x) + lo g_{5} (x^{4}) : lo g_{5} (x^{5})

= \frac{d}{d x} (lo g_{5} (x^{5}))

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 ^{5} )}{ln ( 5 )})

定数を除去:

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

= \frac{1}{ln ( 5 )} \frac{d}{d x} (ln (x^{5}))

連鎖法則を適用:

\frac{1}{x ^{5}} \frac{d}{d x} (x^{5})

= \frac{1}{x ^{5}} \frac{d}{d x} (x^{5})

\frac{d}{d x} (x^{5}) = 5 x^{4}

= \frac{1}{ln ( 5 )} \cdot \frac{1}{x ^{5}} \cdot 5 x^{4}

簡素化

\frac{1}{ln ( 5 )} \cdot \frac{1}{x ^{5}} \cdot 5 x^{4} : \frac{5}{ln ( 5 ) x}

= \frac{5}{ln ( 5 ) x}

グラフ

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