derivative y=(7-3x^3)^3

解答

导数

y = (7 - 3 x^{3})^{3}

- 27 x^{2} (7 - 3 x^{3})^{2}

求解步骤

\frac{d}{d x} ((7 - 3 x^{3})^{3})

使用连锁律:

3 (7 - 3 x^{3})^{2} \frac{d}{d x} (7 - 3 x^{3})

= 3 (7 - 3 x^{3})^{2} \frac{d}{d x} (7 - 3 x^{3})

\frac{d}{d x} (7 - 3 x^{3}) = - 9 x^{2}

= 3 (7 - 3 x^{3})^{2} (- 9 x^{2})

化简

= - 27 x^{2} (7 - 3 x^{3})^{2}