((x+5)e^{1/x})^'

解

((x + 5) e^{\frac{1}{x}})^{^{'}}

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

解答ステップ

((x + 5) e^{\frac{1}{x}})^{'}

積の法則を適用:

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

f = x + 5, g = e^{\frac{1}{x}}

= (x + 5)^{^{'}} e^{\frac{1}{x}} + (e^{\frac{1}{x}})^{^{'}} (x + 5)

(x + 5)^{'} = 1

(e^{\frac{1}{x}})^{'} = - \frac{e ^{\frac{1}{x}}}{x ^{2}}

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

簡素化

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

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