derivative f(x)=x^2+5-3x^{-2}

解答

导数

f (x) = x^{2} + 5 - 3 x^{- 2}

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

求解步骤

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

使用微分加减法定则:

(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}})

化简

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

x \to \infty lim ((\frac{13 x}{13 x + 3})^{5 x})

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

l a pl a ce t r an s f or m (- 2)^{t - 1}

\int \frac{3 x ( e ^{- 2 x} - 7 x )}{5} d x

d er i v a t i v e f (x) = 3 e^{x} + \frac{2}{3 x}