derivative y=(5-2x^3)^3

解

導関数

y = (5 - 2 x^{3})^{3}

- 18 x^{2} (5 - 2 x^{3})^{2}

解答ステップ

\frac{d}{d x} ((5 - 2 x^{3})^{3})

連鎖法則を適用:

3 (5 - 2 x^{3})^{2} \frac{d}{d x} (5 - 2 x^{3})

= 3 (5 - 2 x^{3})^{2} \frac{d}{d x} (5 - 2 x^{3})

\frac{d}{d x} (5 - 2 x^{3}) = - 6 x^{2}

= 3 (5 - 2 x^{3})^{2} (- 6 x^{2})

簡素化

= - 18 x^{2} (5 - 2 x^{3})^{2}