derivative of 2x^7-7x^{-4}+2x^2-3x

解

\frac{d}{d x} (2 x^{7} - 7 x^{- 4} + 2 x^{2} - 3 x)

14 x^{6} + \frac{28}{x ^{5}} + 4 x - 3

解答ステップ

\frac{d}{d x} (2 x^{7} - 7 x^{- 4} + 2 x^{2} - 3 x)

和/差の法則を適用:

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

= \frac{d}{d x} (2 x^{7}) - \frac{d}{d x} (7 x^{- 4}) + \frac{d}{d x} (2 x^{2}) - \frac{d}{d x} (3 x)

\frac{d}{d x} (2 x^{7}) = 14 x^{6}

\frac{d}{d x} (7 x^{- 4}) = - \frac{28}{x ^{5}}

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

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

= 14 x^{6} - (- \frac{28}{x ^{5}}) + 4 x - 3

簡素化

= 14 x^{6} + \frac{28}{x ^{5}} + 4 x - 3