derivative of (4x-1^3(5x+3)^2)

解

\frac{d}{d x} ((4 x - 1)^{3} (5 x + 3)^{2})

12 (4 x - 1)^{2} (5 x + 3)^{2} + 10 (5 x + 3) (4 x - 1)^{3}

解答ステップ

\frac{d}{d x} ((4 x - 1)^{3} (5 x + 3)^{2})

積の法則を適用:

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

f = (4 x - 1)^{3}, g = (5 x + 3)^{2}

= \frac{d}{d x} ((4 x - 1)^{3}) (5 x + 3)^{2} + \frac{d}{d x} ((5 x + 3)^{2}) (4 x - 1)^{3}

\frac{d}{d x} ((4 x - 1)^{3}) = 12 (4 x - 1)^{2}

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

= 12 (4 x - 1)^{2} (5 x + 3)^{2} + 10 (5 x + 3) (4 x - 1)^{3}