derivative (3x-2)^2(3-x^2)^2

解

導関数

(3 x - 2)^{2} (3 - x^{2})^{2}

54 x^{5} - 60 x^{4} - 200 x^{3} + 216 x^{2} + 114 x - 108

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

6 (3 x - 2) (3 - x^{2})^{2} + (- 4 x (3 - x^{2})) (3 x - 2)^{2} : 54 x^{5} - 60 x^{4} - 200 x^{3} + 216 x^{2} + 114 x - 108

= 54 x^{5} - 60 x^{4} - 200 x^{3} + 216 x^{2} + 114 x - 108