What is (\partial)/(\partial x)(xe^y+ye^x) ?

The answer to (\partial)/(\partial x)(xe^y+ye^x) is e^y+ye^x

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(\partial)/(\partial x)(xe^y+ye^x)

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

\int_{0}^{1} \frac{49}{x ^{5}} d x

7 x, at x = 4

\int 8 u^{\frac{9}{8}} d u

x = y^{2} - 2, (- 2, 2)

y^{'} = y (1 - 0.0008 y)

What is (\partial)/(\partial x)(xe^y+ye^x) ?
The answer to (\partial)/(\partial x)(xe^y+ye^x) is e^y+ye^x