(\partial)/(\partial y)((18xy)/(x+y))

解

\frac{\partial}{\partial y} (\frac{18 x y}{x + y})

\frac{18 x ^{2}}{( x + y ) ^{2}}

解答ステップ

\frac{\partial}{\partial y} (\frac{18 x y}{x + y})

x

を定数として扱う

定数を除去:

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

= 18 x \frac{\partial}{\partial y} (\frac{y}{x + y})

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 18 x \frac{\frac{\partial}{\partial y} ( y ) ( x + y ) - \frac{\partial}{\partial y} ( x + y ) y}{( x + y ) ^{2}}

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

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

= 18 x \frac{1 \cdot ( x + y ) - 1 \cdot y}{( x + y ) ^{2}}

簡素化

18 x \frac{1 \cdot ( x + y ) - 1 \cdot y}{( x + y ) ^{2}} : \frac{18 x ^{2}}{( x + y ) ^{2}}

= \frac{18 x ^{2}}{( x + y ) ^{2}}