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})})

Simplify

e^{- (x^{2} + y^{2})} : e^{- x^{2} - y^{2}}

= \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

x \to 8 lim (x - 2)

\int (x + 1)^{\frac{1}{2}} x d x

x \to 2 lim (\frac{7}{( x - 2 ) ^{2}})

cos (x) y^{^{'}} + sin (x) y = 2 cos^{3} (x) sin (x) - 1

x \to \infty lim (3)

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