derivative of x(x-3^2)

解答

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

3 x^{2} - 12 x + 9

求解步骤

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

使用微分乘法定则:

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

f = x, g = (x - 3)^{2}

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

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

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

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

化简

1 \cdot (x - 3)^{2} + 2 (x - 3) x : 3 x^{2} - 12 x + 9

= 3 x^{2} - 12 x + 9