(\partial)/(\partial z)(9ze^{xyz})

解答

\frac{\partial}{\partial z} (9 z e^{x yz})

9 (e^{z x y} + e^{z x y} z x y)

求解步骤

\frac{\partial}{\partial z} (9 z e^{x yz})

将

x, y

视为常数

将常数提出:

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

= 9 \frac{\partial}{\partial z} (z e^{x yz})

使用微分乘法定则:

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

f = z, g = e^{x yz}

= 9 (\frac{\partial}{\partial z} (z) e^{x yz} + \frac{\partial}{\partial z} (e^{x yz}) z)

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

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

= 9 (1 \cdot e^{x yz} + e^{x yz} x yz)

化简

= 9 (e^{z x y} + e^{z x y} z x y)

\frac{d}{d x} ((1 + cos (x)) sin (x))

\frac{\partial}{\partial x} (\frac{1}{5 x ^{4}})

in v erse l a pl a ce \frac{4}{( s + 2 ) ^{3}}

x \to 0 lim ((3 x + 1))

d er i v a t i v e f (x) = lo g_{10} (x)