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受欢迎的微积分 >

(\partial)/(\partial x)(a-bx-c/y+d x/y)

解答

\frac{\partial}{\partial x} (a - b x - \frac{c}{y} + d \frac{x}{y})

解答

- b + \frac{d}{y}

求解步骤

\frac{\partial}{\partial x} (a - b x - \frac{c}{y} + d \frac{x}{y})

化简

a - b x - \frac{c}{y} + d \frac{x}{y} : a - b x + \frac{- c + x d}{y}

= \frac{\partial}{\partial x} (a - b x + \frac{- c + x d}{y})

将

a, b, c, d, y

视为常数

使用微分加减法定则:

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

= \frac{\partial}{\partial x} (a) - \frac{\partial}{\partial x} (b x) + \frac{\partial}{\partial x} (\frac{- c + x d}{y})

\frac{\partial}{\partial x} (a) = 0

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

\frac{\partial}{\partial x} (\frac{- c + x d}{y}) = \frac{d}{y}

= 0 - b + \frac{d}{y}

化简

= - b + \frac{d}{y}

流行的例子

limit as x approaches 2 of 2x^2-x+2

x \to 2 lim (2 x^{2} - x + 2)

(x-y)dx+(x)dy=0

(x - y) d x + (x) d y = 0

y^'+3y=e^{2x}+1

y^{^{'}} + 3 y = e^{2 x} + 1

integral of 2(2+x^2)^{3/2}x

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

斜率 (5-2)(58)

s l o p e (5 - 2) (58)