(\partial)/(\partial x)(x^1y^2+y^4z^5)

解

\frac{\partial}{\partial x} (x^{1} y^{2} + y^{4} z^{5})

y^{2}

解答ステップ

\frac{\partial}{\partial x} (x^{1} y^{2} + y^{4} z^{5})

簡素化

x^{1} y^{2} + y^{4} z^{5} : x y^{2} + y^{4} z^{5}

= \frac{\partial}{\partial x} (x y^{2} + y^{4} z^{5})

y, z

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 y^{2}) + \frac{\partial}{\partial x} (y^{4} z^{5})

\frac{\partial}{\partial x} (x y^{2}) = y^{2}

\frac{\partial}{\partial x} (y^{4} z^{5}) = 0

= y^{2} + 0

簡素化

= y^{2}