derivative y=x^3-14x^2+32x+4

解

導関数

y = x^{3} - 14 x^{2} + 32 x + 4

3 x^{2} - 28 x + 32

解答ステップ

\frac{d}{d x} (x^{3} - 14 x^{2} + 32 x + 4)

和/差の法則を適用:

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

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (14 x^{2}) + \frac{d}{d x} (32 x) + \frac{d}{d x} (4)

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

\frac{d}{d x} (14 x^{2}) = 28 x

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

\frac{d}{d x} (4) = 0

= 3 x^{2} - 28 x + 32 + 0

簡素化

= 3 x^{2} - 28 x + 32