derivative y=(2x^3+7)^2

解答

导数

y = (2 x^{3} + 7)^{2}

12 x^{2} (2 x^{3} + 7)

求解步骤

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

使用连锁律:

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

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

\frac{d}{d x} (2 x^{3} + 7) = 6 x^{2}

= 2 (2 x^{3} + 7) \cdot 6 x^{2}

化简

= 12 x^{2} (2 x^{3} + 7)

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