derivative 6x^4(7-6x)^3

解

導関数

6 x^{4} (7 - 6 x)^{3}

6 (4 x^{3} (7 - 6 x)^{3} - 18 x^{4} (7 - 6 x)^{2})

解答ステップ

\frac{d}{d x} (6 x^{4} (7 - 6 x)^{3})

定数を除去:

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

= 6 \frac{d}{d x} (x^{4} (7 - 6 x)^{3})

積の法則を適用:

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

f = x^{4}, g = (7 - 6 x)^{3}

= 6 (\frac{d}{d x} (x^{4}) (7 - 6 x)^{3} + \frac{d}{d x} ((7 - 6 x)^{3}) x^{4})

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} ((7 - 6 x)^{3}) = - 18 (7 - 6 x)^{2}

= 6 (4 x^{3} (7 - 6 x)^{3} + (- 18 (7 - 6 x)^{2}) x^{4})

簡素化

= 6 (4 x^{3} (7 - 6 x)^{3} - 18 x^{4} (7 - 6 x)^{2})