What is (\partial}{\partial x}(e^{-\frac{x^2)/6-(y^2)/6}) ?

The answer to (\partial}{\partial x}(e^{-\frac{x^2)/6-(y^2)/6}) is -(e^{(-x^2-y^2)/6}x)/(3)

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(\partial}{\partial x}(e^{-\frac{x^2)/6-(y^2)/6})

\frac{\partial}{\partial x} (e^{- \frac{x ^{2}}{6} - \frac{y ^{2}}{6}})

- \frac{e ^{\frac{- x ^{2} - y ^{2}}{6}} x}{3}

Solution steps

\frac{\partial}{\partial x} (e^{- \frac{x ^{2}}{6} - \frac{y ^{2}}{6}})

Simplify

e^{- \frac{x ^{2}}{6} - \frac{y ^{2}}{6}} : e^{\frac{- x ^{2} - y ^{2}}{6}}

= \frac{\partial}{\partial x} (e^{\frac{- x ^{2} - y ^{2}}{6}})

Treat

y

as a constant

Apply the chain rule:

e^{\frac{- x ^{2} - y ^{2}}{6}} \frac{\partial}{\partial x} (\frac{- x ^{2} - y ^{2}}{6})

= e^{\frac{- x ^{2} - y ^{2}}{6}} \frac{\partial}{\partial x} (\frac{- x ^{2} - y ^{2}}{6})

\frac{\partial}{\partial x} (\frac{- x ^{2} - y ^{2}}{6}) = - \frac{x}{3}

= e^{\frac{- x ^{2} - y ^{2}}{6}} (- \frac{x}{3})

Simplify

e^{\frac{- x ^{2} - y ^{2}}{6}} (- \frac{x}{3}) : - \frac{e ^{\frac{- x ^{2} - y ^{2}}{6}} x}{3}

= - \frac{e ^{\frac{- x ^{2} - y ^{2}}{6}} x}{3}

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n = 1 \sum \infty (cos (1.6))^{n}

\int arcsin (2 x) d x

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

x \to 0 - lim (\frac{∣ 8 x ∣}{x})

What is (\partial}{\partial x}(e^{-\frac{x^2)/6-(y^2)/6}) ?
The answer to (\partial}{\partial x}(e^{-\frac{x^2)/6-(y^2)/6}) is -(e^{(-x^2-y^2)/6}x)/(3)