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

The answer to (\partial)/(\partial x)(e^{-6x^2-3y^2}) is -12e^{-6x^2-3y^2}x

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(\partial)/(\partial x)(e^{-6x^2-3y^2})

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

- 12 e^{- 6 x^{2} - 3 y^{2}} x

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (- 6 x^{2} - 3 y^{2}) = - 12 x

= e^{- 6 x^{2} - 3 y^{2}} (- 12 x)

Simplify

= - 12 e^{- 6 x^{2} - 3 y^{2}} x

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What is (\partial)/(\partial x)(e^{-6x^2-3y^2}) ?
The answer to (\partial)/(\partial x)(e^{-6x^2-3y^2}) is -12e^{-6x^2-3y^2}x