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

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

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

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

e^{x + y}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

= e^{x + y} \cdot 1

Simplify

= e^{x + y}

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