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

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

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

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

e^{x - y} x

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

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

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

Simplify

= e^{x - y} x

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