(\partial)/(\partial y)(5/2 x^2+4xy)

解

\frac{\partial}{\partial y} (\frac{5}{2} x^{2} + 4 x y)

4 x

解答ステップ

\frac{\partial}{\partial y} (\frac{5}{2} x^{2} + 4 x y)

簡素化

\frac{5}{2} x^{2} + 4 x y : \frac{5 x ^{2}}{2} + 4 x y

= \frac{\partial}{\partial y} (\frac{5 x ^{2}}{2} + 4 x y)

x

を定数として扱う

和/差の法則を適用:

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

= \frac{\partial}{\partial y} (\frac{5 x ^{2}}{2}) + \frac{\partial}{\partial y} (4 x y)

\frac{\partial}{\partial y} (\frac{5 x ^{2}}{2}) = 0

\frac{\partial}{\partial y} (4 x y) = 4 x

= 0 + 4 x

簡素化

= 4 x