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

解

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

7 x^{6} - 3 x^{2}

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

3 x^{2} (x^{4} - 1) + 4 x^{3} x^{3} : 7 x^{6} - 3 x^{2}

= 7 x^{6} - 3 x^{2}