(\partial)/(\partial x)(1(x-y)e^{1y+5x^2})

解

\frac{\partial}{\partial x} (1 (x - y) e^{1 y + 5 x^{2}})

10 e^{y + 5 x^{2}} x (x - y) + e^{y + 5 x^{2}}

解答ステップ

\frac{\partial}{\partial x} (1 \cdot (x - y) e^{1 \cdot y + 5 x^{2}})

簡素化

1 \cdot (x - y) e^{1 \cdot y + 5 x^{2}} : e^{y + 5 x^{2}} (x - y)

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

y

を定数として扱う

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{y + 5 x^{2}}, g = x - y

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

\frac{\partial}{\partial x} (e^{y + 5 x^{2}}) = e^{y + 5 x^{2}} \cdot 10 x

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

= e^{y + 5 x^{2}} \cdot 10 x (x - y) + 1 \cdot e^{y + 5 x^{2}}

簡素化

= 10 e^{y + 5 x^{2}} x (x - y) + e^{y + 5 x^{2}}