(\partial)/(\partial x)(x^3+zx+10)

解

\frac{\partial}{\partial x} (x^{3} + z x + 10)

3 x^{2} + z

解答ステップ

\frac{\partial}{\partial x} (x^{3} + z x + 10)

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} (z x) + \frac{\partial}{\partial x} (10)

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

\frac{\partial}{\partial x} (z x) = z

\frac{\partial}{\partial x} (10) = 0

= 3 x^{2} + z + 0

簡素化

= 3 x^{2} + z