derivative of x^4-8x^3+22x^2-24x+9

解

\frac{d}{d x} (x^{4} - 8 x^{3} + 22 x^{2} - 24 x + 9)

4 x^{3} - 24 x^{2} + 44 x - 24

解答ステップ

\frac{d}{d x} (x^{4} - 8 x^{3} + 22 x^{2} - 24 x + 9)

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} (22 x^{2}) - \frac{d}{d x} (24 x) + \frac{d}{d x} (9)

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

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

\frac{d}{d x} (22 x^{2}) = 44 x

\frac{d}{d x} (24 x) = 24

\frac{d}{d x} (9) = 0

= 4 x^{3} - 24 x^{2} + 44 x - 24 + 0

簡素化

= 4 x^{3} - 24 x^{2} + 44 x - 24