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

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

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

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

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

- e^{x - y} x

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

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

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

Simplify

= - e^{x - y} x

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