What is (\partial)/(\partial x)(-2e^{-3x^2-y^2}y) ?

The answer to (\partial)/(\partial x)(-2e^{-3x^2-y^2}y) is 12e^{-3x^2-y^2}xy

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(\partial)/(\partial x)(-2e^{-3x^2-y^2}y)

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

12 e^{- 3 x^{2} - y^{2}} x y

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

= 12 e^{- 3 x^{2} - y^{2}} x y

y = 1.00059 e^{(2.39736)} - 1.0005

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What is (\partial)/(\partial x)(-2e^{-3x^2-y^2}y) ?
The answer to (\partial)/(\partial x)(-2e^{-3x^2-y^2}y) is 12e^{-3x^2-y^2}xy