What is the d/(dy)(e^{x-y}) ?

The d/(dy)(e^{x-y}) is -e^{x-y}

What is the first d/(dy)(e^{x-y}) ?

The first d/(dy)(e^{x-y}) is -e^{x-y}

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

- e^{x - y}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

= e^{x - y} (- 1)

Simplify

= - e^{x - y}