derivative of (2-2x^2(3x+1)^2)

解

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

144 x^{3} - 144 x^{2} - 16 x + 16

解答ステップ

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

積の法則を適用:

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

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

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

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

\frac{d}{d x} ((3 x + 1)^{2}) = 6 (3 x + 1)

= (- 4 (2 - 2 x)) (3 x + 1)^{2} + 6 (3 x + 1) (2 - 2 x)^{2}

簡素化

(- 4 (2 - 2 x)) (3 x + 1)^{2} + 6 (3 x + 1) (2 - 2 x)^{2} : 144 x^{3} - 144 x^{2} - 16 x + 16

= 144 x^{3} - 144 x^{2} - 16 x + 16