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

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

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

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

e^{x - y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= e^{x - y} \cdot 1

Simplify

= e^{x - y}

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