derivative of bx^2(x-4)

解

\frac{d}{d x} (b x^{2} (x - 4))

b (3 x^{2} - 8 x)

解答ステップ

\frac{d}{d x} (b x^{2} (x - 4))

定数を除去:

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

= b \frac{d}{d x} (x^{2} (x - 4))

積の法則を適用:

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

f = x^{2}, g = x - 4

= b (\frac{d}{d x} (x^{2}) (x - 4) + \frac{d}{d x} (x - 4) x^{2})

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

\frac{d}{d x} (x - 4) = 1

= b (2 x (x - 4) + 1 \cdot x^{2})

簡素化

b (2 x (x - 4) + 1 \cdot x^{2}) : b (3 x^{2} - 8 x)

= b (3 x^{2} - 8 x)