(\partial)/(\partial y)((5(y+2))/((x+2)^2))

解

\frac{\partial}{\partial y} (\frac{5 ( y + 2 )}{( x + 2 ) ^{2}})

\frac{5}{( x + 2 ) ^{2}}

解答ステップ

\frac{\partial}{\partial y} (\frac{5 ( y + 2 )}{( x + 2 ) ^{2}})

x

を定数として扱う

定数を除去:

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

= \frac{5}{( x + 2 ) ^{2}} \frac{\partial}{\partial y} (y + 2)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{5}{( x + 2 ) ^{2}} (\frac{\partial}{\partial y} (y) + \frac{\partial}{\partial y} (2))

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

\frac{\partial}{\partial y} (2) = 0

= \frac{5}{( x + 2 ) ^{2}} (1 + 0)

簡素化

= \frac{5}{( x + 2 ) ^{2}}