derivative y=5x^2-10x-6x^{-2}

解答

导数

y = 5 x^{2} - 10 x - 6 x^{- 2}

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

求解步骤

\frac{d}{d x} (5 x^{2} - 10 x - 6 x^{- 2})

使用微分加减法定则:

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

= \frac{d}{d x} (5 x^{2}) - \frac{d}{d x} (10 x) - \frac{d}{d x} (6 x^{- 2})

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

\frac{d}{d x} (10 x) = 10

\frac{d}{d x} (6 x^{- 2}) = - \frac{12}{x ^{3}}

= 10 x - 10 - (- \frac{12}{x ^{3}})

化简

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

\frac{d}{d x} (\frac{sin ( x )}{cos ( x )})

\frac{\partial}{\partial x} (- \frac{x - y}{x ^{2} ( x + y )})

d er i v a t i v e f (x) = 2 (13 - x^{4})

\int_{1}^{8} \frac{1}{x 16 x ^{2} - 9} d x

x \to 6 lim (cos (\frac{1}{x - 6}))