(\partial)/(\partial x)((z)(3x^4-2y^3)^3)

解

\frac{\partial}{\partial x} ((z) (3 x^{4} - 2 y^{3})^{3})

36 z x^{3} (3 x^{4} - 2 y^{3})^{2}

解答ステップ

\frac{\partial}{\partial x} ((z) (3 x^{4} - 2 y^{3})^{3})

z, y

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= z \frac{\partial}{\partial x} ((3 x^{4} - 2 y^{3})^{3})

連鎖法則を適用:

3 (3 x^{4} - 2 y^{3})^{2} \frac{\partial}{\partial x} (3 x^{4} - 2 y^{3})

= 3 (3 x^{4} - 2 y^{3})^{2} \frac{\partial}{\partial x} (3 x^{4} - 2 y^{3})

\frac{\partial}{\partial x} (3 x^{4} - 2 y^{3}) = 12 x^{3}

= z \cdot 3 (3 x^{4} - 2 y^{3})^{2} \cdot 12 x^{3}

簡素化

= 36 z x^{3} (3 x^{4} - 2 y^{3})^{2}