(\partial)/(\partial x)((100x)/((x+y)^2))

解

\frac{\partial}{\partial x} (\frac{100 x}{( x + y ) ^{2}})

\frac{100 ( - x + y )}{( x + y ) ^{3}}

解答ステップ

\frac{\partial}{\partial x} (\frac{100 x}{( x + y ) ^{2}})

y

を定数として扱う

定数を除去:

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

= 100 \frac{\partial}{\partial x} (\frac{x}{( x + y ) ^{2}})

商の法則を適用:

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

= 100 \cdot \frac{\frac{\partial}{\partial x} ( x ) ( x + y ) ^{2} - \frac{\partial}{\partial x} ( ( x + y ) ^{2} ) x}{( ( x + y ) ^{2} ) ^{2}}

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

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

= 100 \cdot \frac{1 \cdot ( x + y ) ^{2} - 2 ( x + y ) x}{( ( x + y ) ^{2} ) ^{2}}

簡素化

100 \cdot \frac{1 \cdot ( x + y ) ^{2} - 2 ( x + y ) x}{( ( x + y ) ^{2} ) ^{2}} : \frac{100 ( - x + y )}{( x + y ) ^{3}}

= \frac{100 ( - x + y )}{( x + y ) ^{3}}