derivative x^2(240-x/3)

解

導関数

x^{2} (240 - \frac{x}{3})

480 x - x^{2}

解答ステップ

\frac{d}{d x} (x^{2} (240 - \frac{x}{3}))

積の法則を適用:

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

f = x^{2}, g = 240 - \frac{x}{3}

= \frac{d}{d x} (x^{2}) (240 - \frac{x}{3}) + \frac{d}{d x} (240 - \frac{x}{3}) x^{2}

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

\frac{d}{d x} (240 - \frac{x}{3}) = - \frac{1}{3}

= 2 x (240 - \frac{x}{3}) + (- \frac{1}{3}) x^{2}

簡素化

2 x (240 - \frac{x}{3}) + (- \frac{1}{3}) x^{2} : 480 x - x^{2}

= 480 x - x^{2}