derivative y=(400)/x+7+1/5 x

解答

导数

y = \frac{400}{x} + 7 + \frac{1}{5} x

- \frac{400}{x ^{2}} + \frac{1}{5}

求解步骤

\frac{d}{d x} (\frac{400}{x} + 7 + \frac{1}{5} x)

化简

\frac{400}{x} + 7 + \frac{1}{5} x : \frac{400}{x} + 7 + \frac{x}{5}

= \frac{d}{d x} (\frac{400}{x} + 7 + \frac{x}{5})

使用微分加减法定则:

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

= \frac{d}{d x} (\frac{400}{x}) + \frac{d}{d x} (7) + \frac{d}{d x} (\frac{x}{5})

\frac{d}{d x} (\frac{400}{x}) = - \frac{400}{x ^{2}}

\frac{d}{d x} (7) = 0

\frac{d}{d x} (\frac{x}{5}) = \frac{1}{5}

= - \frac{400}{x ^{2}} + 0 + \frac{1}{5}

化简

= - \frac{400}{x ^{2}} + \frac{1}{5}

x \to 4 lim (2 x - 6)

\frac{d}{d x} (\frac{2}{3} x^{3} - 4 x^{2} + 10 x + 6)

\frac{d y}{d x} = \frac{y}{x}, y (1) = 2

\int_{0}^{10} 200 - 4 x d x

y^{^{'}} = 8 x y, y (1) = 1