derivative y=(2x-1)^5(1-x^4)^4

解

導関数

y = (2 x - 1)^{5} (1 - x^{4})^{4}

10 (2 x - 1)^{4} (1 - x^{4})^{4} - 16 x^{3} (1 - x^{4})^{3} (2 x - 1)^{5}

解答ステップ

\frac{d}{d x} ((2 x - 1)^{5} (1 - x^{4})^{4})

積の法則を適用:

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

f = (2 x - 1)^{5}, g = (1 - x^{4})^{4}

= \frac{d}{d x} ((2 x - 1)^{5}) (1 - x^{4})^{4} + \frac{d}{d x} ((1 - x^{4})^{4}) (2 x - 1)^{5}

\frac{d}{d x} ((2 x - 1)^{5}) = 10 (2 x - 1)^{4}

\frac{d}{d x} ((1 - x^{4})^{4}) = - 16 x^{3} (1 - x^{4})^{3}

= 10 (2 x - 1)^{4} (1 - x^{4})^{4} + (- 16 x^{3} (1 - x^{4})^{3}) (2 x - 1)^{5}

簡素化

= 10 (2 x - 1)^{4} (1 - x^{4})^{4} - 16 x^{3} (1 - x^{4})^{3} (2 x - 1)^{5}