(\partial)/(\partial x)(-x+345sqrt(x+10000))

解答

\frac{\partial}{\partial x} (- x + 345 x + 10000)

- 1 + \frac{345}{2 x + 10000}

求解步骤

\frac{\partial}{\partial x} (- x + 345 x + 10000)

使用微分加减法定则:

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

= - \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (345 x + 10000)

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (345 x + 10000) = \frac{345}{2 x + 10000}

= - 1 + \frac{345}{2 x + 10000}

\frac{\partial}{\partial y} (y e^{\frac{x}{y}})

\frac{\partial}{\partial x} (2 y arctan (x))

y^{^{''}} + 10 y^{^{'}} + 61 y = 0

\frac{d}{d x} (\frac{x + 2 x ^{2}}{1 + x ^{2}})

x \to 4 - lim (\frac{3}{x - 2})