derivative of (2x-1^3(x+1)^5)

解

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

6 (2 x - 1)^{2} (x + 1)^{5} + 5 (x + 1)^{4} (2 x - 1)^{3}

解答ステップ

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

積の法則を適用:

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

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

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

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

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

= 6 (2 x - 1)^{2} (x + 1)^{5} + 5 (x + 1)^{4} (2 x - 1)^{3}