What is (\partial)/(\partial x)(e^{(x+y)}-1) ?

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

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

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

e^{x + y}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (1) = 0

= e^{x + y} - 0

Simplify

= e^{x + y}

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