derivative of x(x-15^2)

解

\frac{d}{d x} (x (x - 15)^{2})

3 x^{2} - 60 x + 225

解答ステップ

\frac{d}{d x} (x (x - 15)^{2})

積の法則を適用:

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

f = x, g = (x - 15)^{2}

= \frac{d x}{d x} (x - 15)^{2} + \frac{d}{d x} ((x - 15)^{2}) x

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

\frac{d}{d x} ((x - 15)^{2}) = 2 (x - 15)

= 1 \cdot (x - 15)^{2} + 2 (x - 15) x

簡素化

1 \cdot (x - 15)^{2} + 2 (x - 15) x : 3 x^{2} - 60 x + 225

= 3 x^{2} - 60 x + 225