(\partial)/(\partial x)(e^y+xe^{xy})

解答

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

e^{y x} + e^{y x} y x

求解步骤

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

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

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

= 0 + e^{y x} + y e^{y x} x

化简

= e^{y x} + e^{y x} y x

d er i v a t i v e x^{3} f (x)

\int_{3}^{6} 4 d x

\frac{\partial}{\partial x} ((x + 2)^{2} - 2 (y - 1)^{2} - 5)

y^{^{''}} + 4 y^{^{'}} + 3 y = x

t an g e n t f (x) = x + 5, at x = 11