(\partial)/(\partial x)((x-1)^2+xy+(y-1)^2)

解答

\frac{\partial}{\partial x} ((x - 1)^{2} + x y + (y - 1)^{2})

2 x + y - 2

求解步骤

\frac{\partial}{\partial x} ((x - 1)^{2} + x y + (y - 1)^{2})

化简

(x - 1)^{2} + x y + (y - 1)^{2} : x^{2} + x y - 2 x + y^{2} + 2 - 2 y

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

将

y

视为常数

使用微分加减法定则:

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

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

\frac{\partial}{\partial x} (x^{2}) = 2 x

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

\frac{\partial}{\partial x} (2 x) = 2

\frac{\partial}{\partial x} (y^{2}) = 0

\frac{\partial}{\partial x} (2) = 0

\frac{\partial}{\partial x} (2 y) = 0

= 2 x + y - 2 + 0 + 0 - 0

化简

= 2 x + y - 2

\int \frac{1}{3 + x ^{2}} d x

x \to 3 lim (\frac{x + 1}{x - 2})

\frac{d}{d x} (14)

\int_{1}^{3} x d x

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