derivative-3x(5x+4)^6

解

導関数

- 3 x (5 x + 4)^{6}

- 3 ((5 x + 4)^{6} + 30 x (5 x + 4)^{5})

解答ステップ

\frac{d}{d x} (- 3 x (5 x + 4)^{6})

定数を除去:

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

= - 3 \frac{d}{d x} (x (5 x + 4)^{6})

積の法則を適用:

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

f = x, g = (5 x + 4)^{6}

= - 3 (\frac{d x}{d x} (5 x + 4)^{6} + \frac{d}{d x} ((5 x + 4)^{6}) x)

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

\frac{d}{d x} ((5 x + 4)^{6}) = 30 (5 x + 4)^{5}

= - 3 (1 \cdot (5 x + 4)^{6} + 30 (5 x + 4)^{5} x)

簡素化

= - 3 ((5 x + 4)^{6} + 30 x (5 x + 4)^{5})