derivative y=2(6x^2-42x+49)

解

導関数

y = 2 (6 x^{2} - 42 x + 49)

2 (12 x - 42)

解答ステップ

\frac{d}{d x} (2 (6 x^{2} - 42 x + 49))

定数を除去:

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

= 2 \frac{d}{d x} (6 x^{2} - 42 x + 49)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 2 (\frac{d}{d x} (6 x^{2}) - \frac{d}{d x} (42 x) + \frac{d}{d x} (49))

\frac{d}{d x} (6 x^{2}) = 12 x

\frac{d}{d x} (42 x) = 42

\frac{d}{d x} (49) = 0

= 2 (12 x - 42 + 0)

簡素化

= 2 (12 x - 42)