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

解

導関数

(2 x - 1)^{2} (x^{3} + 1)^{2}

32 x^{7} - 28 x^{6} + 6 x^{5} + 40 x^{4} - 32 x^{3} + 6 x^{2} + 8 x - 4

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

4 (2 x - 1) (x^{3} + 1)^{2} + 6 x^{2} (x^{3} + 1) (2 x - 1)^{2} : 32 x^{7} - 28 x^{6} + 6 x^{5} + 40 x^{4} - 32 x^{3} + 6 x^{2} + 8 x - 4

= 32 x^{7} - 28 x^{6} + 6 x^{5} + 40 x^{4} - 32 x^{3} + 6 x^{2} + 8 x - 4