derivative y=x^3(8x+12)

解

導関数

y = x^{3} (8 x + 12)

32 x^{3} + 36 x^{2}

解答ステップ

\frac{d}{d x} (x^{3} (8 x + 12))

積の法則を適用:

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

f = x^{3}, g = 8 x + 12

= \frac{d}{d x} (x^{3}) (8 x + 12) + \frac{d}{d x} (8 x + 12) x^{3}

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

\frac{d}{d x} (8 x + 12) = 8

= 3 x^{2} (8 x + 12) + 8 x^{3}

簡素化

3 x^{2} (8 x + 12) + 8 x^{3} : 32 x^{3} + 36 x^{2}

= 32 x^{3} + 36 x^{2}