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

解

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

30 x^{4} - 27 x^{8} + 4 x^{3}

解答ステップ

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

積の法則を適用:

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

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

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

\frac{d}{d x} (3 x^{5} - 1) = 15 x^{4}

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

= 15 x^{4} (2 - x^{4}) + (- 4 x^{3}) (3 x^{5} - 1)

簡素化

15 x^{4} (2 - x^{4}) + (- 4 x^{3}) (3 x^{5} - 1) : 30 x^{4} - 27 x^{8} + 4 x^{3}

= 30 x^{4} - 27 x^{8} + 4 x^{3}