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

The answer to (\partial)/(\partial x)(x/y+e^y) is 1/y

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

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

\frac{1}{y}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (e^{y}) = 0

= \frac{1}{y} + 0

Simplify

= \frac{1}{y}

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