derivative of x^2+5-3x^{-2}

解

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

2 x + \frac{6}{x ^{3}}

解答ステップ

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

和/差の法則を適用:

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

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

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

\frac{d}{d x} (5) = 0

\frac{d}{d x} (3 x^{- 2}) = - \frac{6}{x ^{3}}

= 2 x + 0 - (- \frac{6}{x ^{3}})

簡素化

= 2 x + \frac{6}{x ^{3}}