derivative of 5x-x^{-1/3}-1

解

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

\frac{1}{3 x ^{\frac{4}{3}}} + 5

解答ステップ

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

和/差の法則を適用:

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

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

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

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

\frac{d}{d x} (1) = 0

= 5 - (- \frac{1}{3 x ^{\frac{4}{3}}}) - 0

簡素化

= \frac{1}{3 x ^{\frac{4}{3}}} + 5