(\partial)/(\partial x)(x^4+3^y+x^y)

解

\frac{\partial}{\partial x} (x^{4} + 3^{y} + x^{y})

4 x^{3} + y x^{y - 1}

解答ステップ

\frac{\partial}{\partial x} (x^{4} + 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^{4}) + \frac{\partial}{\partial x} (3^{y}) + \frac{\partial}{\partial x} (x^{y})

\frac{\partial}{\partial x} (x^{4}) = 4 x^{3}

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

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

= 4 x^{3} + 0 + y x^{y - 1}

簡素化

= 4 x^{3} + y x^{y - 1}