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人気のある微分積分 >

derivative f(x)=log_{4}(3x^2+1)

解

導関数

f (x) = lo g_{4} (3 x^{2} + 1)

解

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

解答ステップ

\frac{d}{d x} (lo g_{4} (3 x^{2} + 1))

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 ^{2} + 1 )}{ln ( 4 )})

定数を除去:

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

= \frac{1}{ln ( 4 )} \frac{d}{d x} (ln (3 x^{2} + 1))

連鎖法則を適用:

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

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

\frac{d}{d x} (3 x^{2} + 1) = 6 x

= \frac{1}{ln ( 4 )} \cdot \frac{1}{3 x ^{2} + 1} \cdot 6 x

簡素化

\frac{1}{ln ( 4 )} \cdot \frac{1}{3 x ^{2} + 1} \cdot 6 x : \frac{3 x}{ln ( 2 ) ( 3 x ^{2} + 1 )}

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

グラフ

人気の例

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