derivative f(x)=(4x-x^2)^3

解答

导数

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

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

求解步骤

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

使用连锁律:

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

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

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

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

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