derivative of ce^{y/x}

解

\frac{d}{d x} (c e^{\frac{y}{x}})

\frac{c e ^{\frac{y}{x}} ( x \frac{d y}{d x} - y )}{x ^{2}}

解答ステップ

\frac{d}{d x} (c e^{\frac{y}{x}})

定数を除去:

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

= c \frac{d}{d x} (e^{\frac{y}{x}})

連鎖法則を適用:

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

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

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

= c e^{\frac{y}{x}} \frac{x \frac{d y}{d x} - y}{x ^{2}}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{c e ^{\frac{y}{x}} ( x \frac{d y}{d x} - y )}{x ^{2}}