derivative g(x)=(x-4)^3+3x(x-4)^2

解答

导数

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

12 x^{2} - 72 x + 96

求解步骤

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

化简

(x - 4)^{3} + 3 x (x - 4)^{2} : 4 x^{3} - 36 x^{2} + 96 x - 64

= \frac{d}{d x} (4 x^{3} - 36 x^{2} + 96 x - 64)

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4 x^{3}) - \frac{d}{d x} (36 x^{2}) + \frac{d}{d x} (96 x) - \frac{d}{d x} (64)

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

\frac{d}{d x} (36 x^{2}) = 72 x

\frac{d}{d x} (96 x) = 96

\frac{d}{d x} (64) = 0

= 12 x^{2} - 72 x + 96 - 0

化简

= 12 x^{2} - 72 x + 96

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