(\partial)/(\partial x)(xe^{sqrt(4xy)})

解答

\frac{\partial}{\partial x} (x e^{4 x y})

e^{2 x y} x y + e^{2 x y}

求解步骤

\frac{\partial}{\partial x} (x e^{4 x y})

化简

x e^{4 x y} : e^{2 x y} x

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

将

y

视为常数

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{2 x y}, g = x

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

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

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

= \frac{y e ^{2 y x}}{x} x + 1 \cdot e^{2 x y}

化简

\frac{y e ^{2 y x}}{x} x + 1 \cdot e^{2 x y} : e^{2 x y} x y + e^{2 x y}

= e^{2 x y} x y + e^{2 x y}

l a pl a ce t r an s f or m - sin (3 t)

d er i v a t i v e y = \frac{x ^{3} + 7}{x}

\int \frac{3 v}{1 - 4 v ^{2}} d v

t an g e n t f (x) = x^{5} + 3 x^{2} + 2 x, at x = - 1

t an g e n t 3 x^{2} - 4 x + 6