derivative of (-3x+1^3(2x-1)^4)

解

\frac{d}{d x} ((- 3 x + 1)^{3} (2 x - 1)^{4})

- 9 (- 3 x + 1)^{2} (2 x - 1)^{4} + 8 (2 x - 1)^{3} (- 3 x + 1)^{3}

解答ステップ

\frac{d}{d x} ((- 3 x + 1)^{3} (2 x - 1)^{4})

積の法則を適用:

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

f = (- 3 x + 1)^{3}, g = (2 x - 1)^{4}

= \frac{d}{d x} ((- 3 x + 1)^{3}) (2 x - 1)^{4} + \frac{d}{d x} ((2 x - 1)^{4}) (- 3 x + 1)^{3}

\frac{d}{d x} ((- 3 x + 1)^{3}) = - 9 (- 3 x + 1)^{2}

\frac{d}{d x} ((2 x - 1)^{4}) = 8 (2 x - 1)^{3}

= (- 9 (- 3 x + 1)^{2}) (2 x - 1)^{4} + 8 (2 x - 1)^{3} (- 3 x + 1)^{3}

簡素化

= - 9 (- 3 x + 1)^{2} (2 x - 1)^{4} + 8 (2 x - 1)^{3} (- 3 x + 1)^{3}