derivative f(x)=x^3(2x-1)

解答

导数

f (x) = x^{3} (2 x - 1)

8 x^{3} - 3 x^{2}

求解步骤

\frac{d}{d x} (x^{3} (2 x - 1))

使用微分乘法定则:

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

f = x^{3}, g = 2 x - 1

= \frac{d}{d x} (x^{3}) (2 x - 1) + \frac{d}{d x} (2 x - 1) x^{3}

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

\frac{d}{d x} (2 x - 1) = 2

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

化简

3 x^{2} (2 x - 1) + 2 x^{3} : 8 x^{3} - 3 x^{2}

= 8 x^{3} - 3 x^{2}