derivative of (x^4/4+8/9 x^3-x^2+3x-8)

解

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

x^{3} + \frac{8 x ^{2}}{3} - 2 x + 3

解答ステップ

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

簡素化

\frac{x ^{4}}{4} + \frac{8}{9} x^{3} - x^{2} + 3 x - 8 : \frac{x ^{4}}{4} + \frac{8 x ^{3}}{9} - x^{2} + 3 x - 8

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

和/差の法則を適用:

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

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

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

\frac{d}{d x} (\frac{8 x ^{3}}{9}) = \frac{8 x ^{2}}{3}

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

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

\frac{d}{d x} (8) = 0

= x^{3} + \frac{8 x ^{2}}{3} - 2 x + 3 - 0

簡素化

= x^{3} + \frac{8 x ^{2}}{3} - 2 x + 3