(\partial)/(\partial x)(x^7+3^y+x^y)

解

\frac{\partial}{\partial x} (x^{7} + 3^{y} + x^{y})

7 x^{6} + y x^{y - 1}

解答ステップ

\frac{\partial}{\partial x} (x^{7} + 3^{y} + x^{y})

y

を定数として扱う

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x^{7}) + \frac{\partial}{\partial x} (3^{y}) + \frac{\partial}{\partial x} (x^{y})

\frac{\partial}{\partial x} (x^{7}) = 7 x^{6}

\frac{\partial}{\partial x} (3^{y}) = 0

\frac{\partial}{\partial x} (x^{y}) = y x^{y - 1}

= 7 x^{6} + 0 + y x^{y - 1}

簡素化

= 7 x^{6} + y x^{y - 1}