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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\int_{1}^{4} ln (x) d x

f (x) = x^{2} + 6 x - 5, at x = 2

\int 12 (y^{4} + 4 y^{2} + 1)^{2} (y^{3} + 2 y) d y

\frac{x}{x + 3}

\int 6 x + 1 d x

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