(\partial)/(\partial x)((x+y)e^x)

解答

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

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

求解步骤

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

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

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

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

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

化简

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

\int \frac{1}{P} d P

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\frac{d}{d x} (x + 2 sin (x))

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x \to 7 - lim (\frac{∣ x - 7 ∣}{x - 7})