derivative of 11e^{1/x}

解

\frac{d}{d x} (11 e^{\frac{1}{x}})

- \frac{11 e ^{\frac{1}{x}}}{x ^{2}}

解答ステップ

\frac{d}{d x} (11 e^{\frac{1}{x}})

定数を除去:

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

= 11 \frac{d}{d x} (e^{\frac{1}{x}})

連鎖法則を適用:

e^{\frac{1}{x}} \frac{d}{d x} (\frac{1}{x})

= e^{\frac{1}{x}} \frac{d}{d x} (\frac{1}{x})

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

= 11 e^{\frac{1}{x}} (- \frac{1}{x ^{2}})

簡素化

11 e^{\frac{1}{x}} (- \frac{1}{x ^{2}}) : - \frac{11 e ^{\frac{1}{x}}}{x ^{2}}

= - \frac{11 e ^{\frac{1}{x}}}{x ^{2}}