derivative of (x^3-1^4)

解答

\frac{d}{d x} ((x^{3} - 1)^{4})

12 x^{2} (x^{3} - 1)^{3}

求解步骤

\frac{d}{d x} ((x^{3} - 1)^{4})

使用连锁律:

4 (x^{3} - 1)^{3} \frac{d}{d x} (x^{3} - 1)

= 4 (x^{3} - 1)^{3} \frac{d}{d x} (x^{3} - 1)

\frac{d}{d x} (x^{3} - 1) = 3 x^{2}

= 4 (x^{3} - 1)^{3} \cdot 3 x^{2}

化简

= 12 x^{2} (x^{3} - 1)^{3}

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