derivative of (3x^2-6x+10(x^3))

解

\frac{d}{d x} ((3 x^{2} - 6 x + 10) (x^{3}))

15 x^{4} - 24 x^{3} + 30 x^{2}

解答ステップ

\frac{d}{d x} ((3 x^{2} - 6 x + 10) (x^{3}))

積の法則を適用:

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

f = 3 x^{2} - 6 x + 10, g = x^{3}

= \frac{d}{d x} (3 x^{2} - 6 x + 10) x^{3} + \frac{d}{d x} (x^{3}) (3 x^{2} - 6 x + 10)

\frac{d}{d x} (3 x^{2} - 6 x + 10) = 6 x - 6

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

= (6 x - 6) x^{3} + 3 x^{2} (3 x^{2} - 6 x + 10)

簡素化

(6 x - 6) x^{3} + 3 x^{2} (3 x^{2} - 6 x + 10) : 15 x^{4} - 24 x^{3} + 30 x^{2}

= 15 x^{4} - 24 x^{3} + 30 x^{2}