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受欢迎的微积分 >

(\partial)/(\partial x)(9xe^{2xy})

解答

\frac{\partial}{\partial x} (9 x e^{2 x y})

解答

9 (e^{2 x y} + 2 e^{2 x y} x y)

求解步骤

\frac{\partial}{\partial x} (9 x e^{2 x y})

将

y

视为常数

将常数提出:

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

= 9 \frac{\partial}{\partial x} (x e^{2 x y})

使用微分乘法定则:

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

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

= 9 (\frac{\partial}{\partial x} (x) e^{2 x y} + \frac{\partial}{\partial x} (e^{2 x y}) x)

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

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

= 9 (1 \cdot e^{2 x y} + e^{2 x y} \cdot 2 y x)

化简

= 9 (e^{2 x y} + 2 e^{2 x y} x y)

流行的例子

inverselaplace (s^2+2s+5)/(s^2(s+1))

in v erse l a pl a ce \frac{s ^{2} + 2 s + 5}{s ^{2} ( s + 1 )}

麦克劳林 e^{iθ}

ma c l a u r in e^{i θ}

\frac{d}{d z} (e^{i z})

\frac{d y}{d t} = 1.7 y

derivative f(x)=(x-5)(x+1)

d er i v a t i v e f (x) = (x - 5) (x + 1)