(\partial)/(\partial w)(te^{w/t})

解

\frac{\partial}{\partial w} (t e^{\frac{w}{t}})

e^{\frac{w}{t}}

解答ステップ

\frac{\partial}{\partial w} (t e^{\frac{w}{t}})

t

を定数として扱う

定数を除去:

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

= t \frac{\partial}{\partial w} (e^{\frac{w}{t}})

連鎖法則を適用:

e^{\frac{w}{t}} \frac{\partial}{\partial w} (\frac{w}{t})

= e^{\frac{w}{t}} \frac{\partial}{\partial w} (\frac{w}{t})

\frac{\partial}{\partial w} (\frac{w}{t}) = \frac{1}{t}

= t e^{\frac{w}{t}} \frac{1}{t}

簡素化

t e^{\frac{w}{t}} \frac{1}{t} : e^{\frac{w}{t}}

= e^{\frac{w}{t}}