What is (\partial)/(\partial x)(e^{(-0.1xy)}) ?

The answer to (\partial)/(\partial x)(e^{(-0.1xy)}) is -0.1e^{-0.1xy}y

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(\partial)/(\partial x)(e^{(-0.1xy)})

\frac{\partial}{\partial x} (e^{(- 0.1 x y)})

- 0.1 e^{- 0.1 x y} y

Solution steps

\frac{\partial}{\partial x} (e^{(- 0.1 x y)})

Treat

y

as a constant

Apply the chain rule:

e^{- 0.1 x y} \frac{\partial}{\partial x} (- 0.1 x y)

= e^{- 0.1 x y} \frac{\partial}{\partial x} (- 0.1 x y)

\frac{\partial}{\partial x} (- 0.1 x y) = - 0.1 y

= e^{- 0.1 x y} (- 0.1 y)

Simplify

= - 0.1 e^{- 0.1 x y} y

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What is (\partial)/(\partial x)(e^{(-0.1xy)}) ?
The answer to (\partial)/(\partial x)(e^{(-0.1xy)}) is -0.1e^{-0.1xy}y