derivative f(x)=(2x^2-4)^4

解答

导数

f (x) = (2 x^{2} - 4)^{4}

16 x (2 x^{2} - 4)^{3}

求解步骤

\frac{d}{d x} ((2 x^{2} - 4)^{4})

使用连锁律:

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

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

\frac{d}{d x} (2 x^{2} - 4) = 4 x

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

化简

= 16 x (2 x^{2} - 4)^{3}

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