derivative y=(2x-3)(x+3)^3

解

導関数

y = (2 x - 3) (x + 3)^{3}

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

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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