derivative of (x-2^4-1)

解

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

4 x^{3} - 24 x^{2} + 48 x - 32

解答ステップ

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

簡素化

(x - 2)^{4} - 1 : x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 15

= \frac{d}{d x} (x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 15)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{4}) - \frac{d}{d x} (8 x^{3}) + \frac{d}{d x} (24 x^{2}) - \frac{d}{d x} (32 x) + \frac{d}{d x} (15)

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

\frac{d}{d x} (8 x^{3}) = 24 x^{2}

\frac{d}{d x} (24 x^{2}) = 48 x

\frac{d}{d x} (32 x) = 32

\frac{d}{d x} (15) = 0

= 4 x^{3} - 24 x^{2} + 48 x - 32 + 0

簡素化

= 4 x^{3} - 24 x^{2} + 48 x - 32