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

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

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

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

- e^{- x y} x

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) = - x

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

Simplify

= - e^{- x y} x

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