(\partial)/(\partial x)(e^{6xe^y})

解

\frac{\partial}{\partial x} (e^{6 x e^{y}})

6 e^{6 e^{y} x + y}

解答ステップ

\frac{\partial}{\partial x} (e^{6 x e^{y}})

y

を定数として扱う

連鎖法則を適用:

e^{6 x e^{y}} \frac{\partial}{\partial x} (6 x e^{y})

= e^{6 x e^{y}} \frac{\partial}{\partial x} (6 x e^{y})

\frac{\partial}{\partial x} (6 x e^{y}) = 6 e^{y}

= e^{6 x e^{y}} \cdot 6 e^{y}

指数の規則を適用する:

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

e^{6 x e^{y}} e^{y} = e^{6 e^{y} x + y}

= 6 e^{6 e^{y} x + y}