derivative y=(6x-5)^2(3-x^5)^2

解

導関数

y = (6 x - 5)^{2} (3 - x^{5})^{2}

432 x^{11} - 660 x^{10} + 250 x^{9} - 1512 x^{6} + 2160 x^{5} - 750 x^{4} + 648 x - 540

解答ステップ

\frac{d}{d x} ((6 x - 5)^{2} (3 - x^{5})^{2})

積の法則を適用:

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

f = (6 x - 5)^{2}, g = (3 - x^{5})^{2}

= \frac{d}{d x} ((6 x - 5)^{2}) (3 - x^{5})^{2} + \frac{d}{d x} ((3 - x^{5})^{2}) (6 x - 5)^{2}

\frac{d}{d x} ((6 x - 5)^{2}) = 12 (6 x - 5)

\frac{d}{d x} ((3 - x^{5})^{2}) = - 10 x^{4} (3 - x^{5})

= 12 (6 x - 5) (3 - x^{5})^{2} + (- 10 x^{4} (3 - x^{5})) (6 x - 5)^{2}

簡素化

12 (6 x - 5) (3 - x^{5})^{2} + (- 10 x^{4} (3 - x^{5})) (6 x - 5)^{2} : 432 x^{11} - 660 x^{10} + 250 x^{9} - 1512 x^{6} + 2160 x^{5} - 750 x^{4} + 648 x - 540

= 432 x^{11} - 660 x^{10} + 250 x^{9} - 1512 x^{6} + 2160 x^{5} - 750 x^{4} + 648 x - 540