derivative f(2)=4log_{6}(x)

解

導関数

f (2) = 4 lo g_{6} (x)

\frac{4}{ln ( 6 ) x}

解答ステップ

\frac{d}{d x} (4 lo g_{6} (x))

定数を除去:

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

= 4 \frac{d}{d x} (lo g_{6} (x))

導関数ログの法則を適用:

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

= 4 \cdot \frac{1}{x ln ( 6 )}

簡素化

4 \cdot \frac{1}{x ln ( 6 )} : \frac{4}{ln ( 6 ) x}

= \frac{4}{ln ( 6 ) x}