(\partial)/(\partial x)(x^3+y^3+z^3+6xyz)

解

\frac{\partial}{\partial x} (x^{3} + y^{3} + z^{3} + 6 x yz)

3 x^{2} + 6 yz

解答ステップ

\frac{\partial}{\partial x} (x^{3} + y^{3} + z^{3} + 6 x yz)

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^{3}) + \frac{\partial}{\partial x} (y^{3}) + \frac{\partial}{\partial x} (z^{3}) + \frac{\partial}{\partial x} (6 x yz)

\frac{\partial}{\partial x} (x^{3}) = 3 x^{2}

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

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

\frac{\partial}{\partial x} (6 x yz) = 6 yz

= 3 x^{2} + 0 + 0 + 6 yz

簡素化

= 3 x^{2} + 6 yz