What is (\partial)/(\partial x)(xy+xe^{y/x}) ?

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

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(\partial)/(\partial x)(xy+xe^{y/x})

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

y + e^{\frac{y}{x}} - \frac{y e ^{\frac{y}{x}}}{x}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= y + e^{\frac{y}{x}} - \frac{y e ^{\frac{y}{x}}}{x}

\int 8 t e^{t} d t

4 \frac{d y}{d x} + 20 y = 5

\int \frac{2}{- x} d x

\frac{d}{d x} (2 csc (2 x))

\frac{\partial}{\partial y} (sin (x \cdot y))

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