derivative of 1/3 x^3-5x-4/x

解

\frac{d}{d x} (\frac{1}{3} x^{3} - 5 x - \frac{4}{x})

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

解答ステップ

\frac{d}{d x} (\frac{1}{3} x^{3} - 5 x - \frac{4}{x})

簡素化

\frac{1}{3} x^{3} - 5 x - \frac{4}{x} : \frac{x ^{3}}{3} - 5 x - \frac{4}{x}

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

和/差の法則を適用:

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

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

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

\frac{d}{d x} (5 x) = 5

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

= x^{2} - 5 - (- \frac{4}{x ^{2}})

簡素化

= x^{2} - 5 + \frac{4}{x ^{2}}