derivative of (3x-1^5(1-3x)^4)

解

\frac{d}{d x} ((3 x - 1)^{5} (1 - 3 x)^{4})

15 (3 x - 1)^{4} (1 - 3 x)^{4} - 12 (1 - 3 x)^{3} (3 x - 1)^{5}

解答ステップ

\frac{d}{d x} ((3 x - 1)^{5} (1 - 3 x)^{4})

積の法則を適用:

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

f = (3 x - 1)^{5}, g = (1 - 3 x)^{4}

= \frac{d}{d x} ((3 x - 1)^{5}) (1 - 3 x)^{4} + \frac{d}{d x} ((1 - 3 x)^{4}) (3 x - 1)^{5}

\frac{d}{d x} ((3 x - 1)^{5}) = 15 (3 x - 1)^{4}

\frac{d}{d x} ((1 - 3 x)^{4}) = - 12 (1 - 3 x)^{3}

= 15 (3 x - 1)^{4} (1 - 3 x)^{4} + (- 12 (1 - 3 x)^{3}) (3 x - 1)^{5}

簡素化

= 15 (3 x - 1)^{4} (1 - 3 x)^{4} - 12 (1 - 3 x)^{3} (3 x - 1)^{5}