What is (\partial)/(\partial x)(e^{-x^2-y^2}) ?

The answer to (\partial)/(\partial x)(e^{-x^2-y^2}) is -2e^{-x^2-y^2}x

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(\partial)/(\partial x)(e^{-x^2-y^2})

\frac{\partial}{\partial x} (e^{- x^{2} - y^{2}})

- 2 e^{- x^{2} - y^{2}} x

Solution steps

\frac{\partial}{\partial x} (e^{- x^{2} - y^{2}})

Treat

y

as a constant

Apply the chain rule:

e^{- x^{2} - y^{2}} \frac{\partial}{\partial x} (- x^{2} - y^{2})

= e^{- x^{2} - y^{2}} \frac{\partial}{\partial x} (- x^{2} - y^{2})

\frac{\partial}{\partial x} (- x^{2} - y^{2}) = - 2 x

= e^{- x^{2} - y^{2}} (- 2 x)

Simplify

= - 2 e^{- x^{2} - y^{2}} x

What is (\partial)/(\partial x)(e^{-x^2-y^2}) ?
The answer to (\partial)/(\partial x)(e^{-x^2-y^2}) is -2e^{-x^2-y^2}x