(\partial)/(\partial x)(xzsqrt(x+y))

解答

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

\frac{z ( 3 x + 2 y )}{2 x + y}

求解步骤

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

将

z, y

视为常数

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用微分乘法定则:

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

f = x, g = x + y

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

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

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

= z (1 \cdot x + y + \frac{1}{2 x + y} x)

化简

z (1 \cdot x + y + \frac{1}{2 x + y} x) : \frac{z ( 3 x + 2 y )}{2 x + y}

= \frac{z ( 3 x + 2 y )}{2 x + y}

\int - 5 x^{4} e^{x^{5}} d x

d er i v a t i v e f (x) = \frac{x}{32} (x + 3 x)

\frac{\partial}{\partial y} (sin (x^{2} y))

\frac{d}{d x} ((x^{3} + 6 x)^{4})

in v erse l a pl a ce \frac{2 e ^{- 2 s}}{3 s ^{2} + 12}