derivative of-3x^5+4x^{-3}-5x^{-2}+5

解答

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

- 15 x^{4} + \frac{10}{x ^{3}} - \frac{12}{x ^{4}}

求解步骤

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

使用微分加减法定则:

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

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

\frac{d}{d x} (3 x^{5}) = 15 x^{4}

\frac{d}{d x} (4 x^{- 3}) = - \frac{12}{x ^{4}}

\frac{d}{d x} (5 x^{- 2}) = - \frac{10}{x ^{3}}

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

= - 15 x^{4} - \frac{12}{x ^{4}} - (- \frac{10}{x ^{3}}) + 0

化简

= - 15 x^{4} + \frac{10}{x ^{3}} - \frac{12}{x ^{4}}

x \to \infty lim (\frac{x}{2 a})

\frac{\partial}{\partial x} (\frac{x}{R ( x )})

n = 2 \sum \infty \frac{3}{7 ^{n}}

in v erse l a pl a ce \frac{s}{10 ( s ^{2} + 10 s + 9.8 )}

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