(\partial)/(\partial x)(blog_{10}(x))

解

\frac{\partial}{\partial x} (b lo g_{10} (x))

\frac{b}{ln ( 10 ) x}

解答ステップ

\frac{\partial}{\partial x} (b lo g_{10} (x))

b

を定数として扱う

定数を除去:

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

= b \frac{\partial}{\partial x} (lo g_{10} (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 )}

= b \frac{1}{x ln ( 10 )}

簡素化

b \frac{1}{x ln ( 10 )} : \frac{b}{ln ( 10 ) x}

= \frac{b}{ln ( 10 ) x}