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

解答

导数

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

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

求解步骤

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

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = (x - 4)^{3}

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

\frac{d x}{d x} = 1

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

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

化简

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