(\partial)/(\partial x)(12x+6y-x^2+xy-y^2)

解答

\frac{\partial}{\partial x} (12 x + 6 y - x^{2} + x y - y^{2})

y + 12 - 2 x

求解步骤

\frac{\partial}{\partial x} (12 x + 6 y - x^{2} + x y - y^{2})

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} (12 x) + \frac{\partial}{\partial x} (6 y) - \frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (x y) - \frac{\partial}{\partial x} (y^{2})

\frac{\partial}{\partial x} (12 x) = 12

\frac{\partial}{\partial x} (6 y) = 0

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

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

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

= 12 + 0 - 2 x + y - 0

化简

= y + 12 - 2 x

t an g e n t 7 x - 6

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

\frac{d}{d x} (7 + x sec (x))

\int x e^{- x} d x

\frac{d}{d x} (ccos t + t^{2} sin (t))