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

解

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

8 (4 x + 1) (1 - x)^{3} - 3 (1 - x)^{2} (4 x + 1)^{2}

解答ステップ

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

積の法則を適用:

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

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

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

\frac{d}{d x} ((4 x + 1)^{2}) = 8 (4 x + 1)

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

= 8 (4 x + 1) (1 - x)^{3} + (- 3 (1 - x)^{2}) (4 x + 1)^{2}

簡素化

= 8 (4 x + 1) (1 - x)^{3} - 3 (1 - x)^{2} (4 x + 1)^{2}