(\partial)/(\partial x)(e^{9xe^y})

解

\frac{\partial}{\partial x} (e^{9 x e^{y}})

9 e^{9 e^{y} x + y}

解答ステップ

\frac{\partial}{\partial x} (e^{9 x e^{y}})

y

を定数として扱う

連鎖法則を適用:

e^{9 x e^{y}} \frac{\partial}{\partial x} (9 x e^{y})

= e^{9 x e^{y}} \frac{\partial}{\partial x} (9 x e^{y})

\frac{\partial}{\partial x} (9 x e^{y}) = 9 e^{y}

= e^{9 x e^{y}} \cdot 9 e^{y}

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

e^{9 x e^{y}} e^{y} = e^{9 e^{y} x + y}

= 9 e^{9 e^{y} x + y}