derivative of (-3x^5-x^4-x^3+4x^2/(x^2))

解

\frac{d}{d x} (\frac{- 3 x ^{5} - x ^{4} - x ^{3} + 4 x ^{2}}{x ^{2}})

- 9 x^{2} - 2 x - 1

解答ステップ

\frac{d}{d x} (\frac{- 3 x ^{5} - x ^{4} - x ^{3} + 4 x ^{2}}{x ^{2}})

簡素化

\frac{- 3 x ^{5} - x ^{4} - x ^{3} + 4 x ^{2}}{x ^{2}} : - 3 x^{3} - x^{2} - x + 4

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

和/差の法則を適用:

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

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

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

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

\frac{d x}{d x} = 1

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

= - 9 x^{2} - 2 x - 1 + 0

簡素化

= - 9 x^{2} - 2 x - 1