derivative of 3x(6x-5x^2)

解

\frac{d}{d x} (3 x (6 x - 5 x^{2}))

3 (- 15 x^{2} + 12 x)

解答ステップ

\frac{d}{d x} (3 x (6 x - 5 x^{2}))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (x (6 x - 5 x^{2}))

積の法則を適用:

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

f = x, g = 6 x - 5 x^{2}

= 3 (\frac{d x}{d x} (6 x - 5 x^{2}) + \frac{d}{d x} (6 x - 5 x^{2}) x)

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

\frac{d}{d x} (6 x - 5 x^{2}) = 6 - 10 x

= 3 (1 \cdot (6 x - 5 x^{2}) + (6 - 10 x) x)

簡素化

3 (1 \cdot (6 x - 5 x^{2}) + (6 - 10 x) x) : 3 (- 15 x^{2} + 12 x)

= 3 (- 15 x^{2} + 12 x)