What is (\partial)/(\partial x)(xy+xe^{1/y}) ?

The answer to (\partial)/(\partial x)(xy+xe^{1/y}) is y+e^{1/y}

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(\partial)/(\partial x)(xy+xe^{1/y})

\frac{\partial}{\partial x} (x y + x e^{\frac{1}{y}})

y + e^{\frac{1}{y}}

Solution steps

\frac{\partial}{\partial x} (x y + x e^{\frac{1}{y}})

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{1}{y}})

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

\frac{\partial}{\partial x} (x e^{\frac{1}{y}}) = e^{\frac{1}{y}}

= y + e^{\frac{1}{y}}

\int sec^{2} (u) d u

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\int x^{3} cos (12 x) d x

x \to 0 lim (\frac{x - 1}{x ^{2} + 1})

What is (\partial)/(\partial x)(xy+xe^{1/y}) ?
The answer to (\partial)/(\partial x)(xy+xe^{1/y}) is y+e^{1/y}