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人気のある微分積分 >

derivative log_{10}(x^2+3)

解

導関数

lo g_{10} (x^{2} + 3)

解

\frac{2 x}{ln ( 10 ) ( x ^{2} + 3 )}

解答ステップ

\frac{d}{d x} (lo g_{10} (x^{2} + 3))

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 ^{2} + 3 )}{ln ( 10 )})

定数を除去:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (x^{2} + 3))

連鎖法則を適用:

\frac{1}{x ^{2} + 3} \frac{d}{d x} (x^{2} + 3)

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

\frac{d}{d x} (x^{2} + 3) = 2 x

= \frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{2} + 3} \cdot 2 x

簡素化

\frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{2} + 3} \cdot 2 x : \frac{2 x}{ln ( 10 ) ( x ^{2} + 3 )}

= \frac{2 x}{ln ( 10 ) ( x ^{2} + 3 )}

グラフ

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