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

\frac{d}{d x} ((5 x^{2} + x + 9) tan (7 x))

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

x \to 5 - lim (\frac{- 2}{x ^{2} - 25})

\int sin (2 x + y) - sin (x + y) d x

f (x) = x^{\frac{6}{5}}

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