derivative (4x-5)^3(1-x^5)^2

解

導関数

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

12 (4 x - 5)^{2} (1 - x^{5})^{2} - 10 x^{4} (1 - x^{5}) (4 x - 5)^{3}

解答ステップ

\frac{d}{d x} ((4 x - 5)^{3} (1 - x^{5})^{2})

積の法則を適用:

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

f = (4 x - 5)^{3}, g = (1 - x^{5})^{2}

= \frac{d}{d x} ((4 x - 5)^{3}) (1 - x^{5})^{2} + \frac{d}{d x} ((1 - x^{5})^{2}) (4 x - 5)^{3}

\frac{d}{d x} ((4 x - 5)^{3}) = 12 (4 x - 5)^{2}

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

= 12 (4 x - 5)^{2} (1 - x^{5})^{2} + (- 10 x^{4} (1 - x^{5})) (4 x - 5)^{3}

簡素化

= 12 (4 x - 5)^{2} (1 - x^{5})^{2} - 10 x^{4} (1 - x^{5}) (4 x - 5)^{3}