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

解

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

5 x^{4} - 4 x^{3} - 24 x^{2} + 16 x + 16

解答ステップ

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

積の法則を適用:

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

f = (x^{2} - 4)^{2}, g = x - 1

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

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

\frac{d}{d x} (x - 1) = 1

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

簡素化

4 x (x^{2} - 4) (x - 1) + 1 \cdot (x^{2} - 4)^{2} : 5 x^{4} - 4 x^{3} - 24 x^{2} + 16 x + 16

= 5 x^{4} - 4 x^{3} - 24 x^{2} + 16 x + 16