derivative x^2(120-x)

解答

导数

x^{2} (120 - x)

240 x - 3 x^{2}

求解步骤

\frac{d}{d x} (x^{2} (120 - x))

使用微分乘法定则:

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

f = x^{2}, g = 120 - x

= \frac{d}{d x} (x^{2}) (120 - x) + \frac{d}{d x} (120 - x) x^{2}

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

\frac{d}{d x} (120 - x) = - 1

= 2 x (120 - x) + (- 1) x^{2}

化简

2 x (120 - x) + (- 1) x^{2} : 240 x - 3 x^{2}

= 240 x - 3 x^{2}

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