derivative y=x^3-8x^2+4x-32

解

導関数

y = x^{3} - 8 x^{2} + 4 x - 32

3 x^{2} - 16 x + 4

解答ステップ

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

和/差の法則を適用:

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

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

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

\frac{d}{d x} (8 x^{2}) = 16 x

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

\frac{d}{d x} (32) = 0

= 3 x^{2} - 16 x + 4 - 0

簡素化

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