(\partial)/(\partial x)(xy{E}(x,y)(x,y)^{x/y})

解

\frac{\partial}{\partial x} (x y E (x, y) (x, y)^{\frac{x}{y}})

y (1 \cdot E (x, y) (x, y)^{\frac{x}{y}} + (\frac{\partial}{\partial x} (E (x, y)) (x, y)^{\frac{x}{y}} + e^{\frac{x}{y} l n (x, y)} \frac{1}{y} (1 \cdot ln (x, y) + \frac{1}{x , y} (, y \cdot 1) x) E (x, y)) x)

解答ステップ

\frac{\partial}{\partial x} (x y E (x, y) (x, y)^{\frac{x}{y}})

y

を定数として扱う

定数を除去:

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

= y \frac{\partial}{\partial x} (x E (x, y) (x, y)^{\frac{x}{y}})

積の法則を適用:

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

f = x, g = E (x, y) (x, y)^{\frac{x}{y}}

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

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

\frac{\partial}{\partial x} (E (x, y) (x, y)^{\frac{x}{y}}) = \frac{\partial}{\partial x} (E (x, y)) (x, y)^{\frac{x}{y}} + e^{\frac{x}{y} l n (x, y)} \frac{1}{y} (1 \cdot ln (x, y) + \frac{1}{x , y} (, y \cdot 1) x) E (x, y)

= y (1 \cdot E (x, y) (x, y)^{\frac{x}{y}} + (\frac{\partial}{\partial x} (E (x, y)) (x, y)^{\frac{x}{y}} + e^{\frac{x}{y} l n (x, y)} \frac{1}{y} (1 \cdot ln (x, y) + \frac{1}{x , y} (, y \cdot 1) x) E (x, y)) x)