derivative f(x)=5(x^3-x)^4

解

導関数

f (x) = 5 (x^{3} - x)^{4}

20 (x^{3} - x)^{3} (3 x^{2} - 1)

解答ステップ

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

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

連鎖法則を適用:

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

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

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

= 5 \cdot 4 (x^{3} - x)^{3} (3 x^{2} - 1)

簡素化

= 20 (x^{3} - x)^{3} (3 x^{2} - 1)