(\partial)/(\partial x)(log_{10}(x+y))

解

\frac{\partial}{\partial x} (lo g_{10} (x + y))

\frac{1}{ln ( 10 ) ( x + y )}

解答ステップ

\frac{\partial}{\partial x} (lo g_{10} (x + y))

y

を定数として扱う

対数の規則を適用する:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{\partial}{\partial x} (\frac{ln ( x + y )}{ln ( 10 )})

定数を除去:

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

= \frac{1}{ln ( 10 )} \frac{\partial}{\partial x} (ln (x + y))

連鎖法則を適用:

\frac{1}{x + y} \frac{\partial}{\partial x} (x + y)

= \frac{1}{x + y} \frac{\partial}{\partial x} (x + y)

\frac{\partial}{\partial x} (x + y) = 1

= \frac{1}{ln ( 10 )} \cdot \frac{1}{x + y} \cdot 1

簡素化

\frac{1}{ln ( 10 )} \cdot \frac{1}{x + y} \cdot 1 : \frac{1}{ln ( 10 ) ( x + y )}

= \frac{1}{ln ( 10 ) ( x + y )}