What is (\partial)/(\partial x)(e^{1-xy}) ?

The answer to (\partial)/(\partial x)(e^{1-xy}) is -e^{1-xy}y

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(\partial)/(\partial x)(e^{1-xy})

\frac{\partial}{\partial x} (e^{1 - x y})

- e^{1 - x y} y

Solution steps

\frac{\partial}{\partial x} (e^{1 - x y})

Treat

y

as a constant

Apply the chain rule:

e^{1 - x y} \frac{\partial}{\partial x} (1 - x y)

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

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

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

Simplify

= - e^{1 - x y} y

What is (\partial)/(\partial x)(e^{1-xy}) ?
The answer to (\partial)/(\partial x)(e^{1-xy}) is -e^{1-xy}y