What is (\partial)/(\partial x)(1000e^{-x^2-2y^2-z^2}) ?

The answer to (\partial)/(\partial x)(1000e^{-x^2-2y^2-z^2}) is -2000e^{-x^2-2y^2-z^2}x

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(\partial)/(\partial x)(1000e^{-x^2-2y^2-z^2})

\frac{\partial}{\partial x} (1000 e^{- x^{2} - 2 y^{2} - z^{2}})

- 2000 e^{- x^{2} - 2 y^{2} - z^{2}} x

Solution steps

\frac{\partial}{\partial x} (1000 e^{- x^{2} - 2 y^{2} - z^{2}})

Treat

y, z

as constants

Take the constant out:

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

= 1000 \frac{\partial}{\partial x} (e^{- x^{2} - 2 y^{2} - z^{2}})

Apply the chain rule:

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

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

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

= 1000 e^{- x^{2} - 2 y^{2} - z^{2}} (- 2 x)

Simplify

= - 2000 e^{- x^{2} - 2 y^{2} - z^{2}} x

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What is (\partial)/(\partial x)(1000e^{-x^2-2y^2-z^2}) ?
The answer to (\partial)/(\partial x)(1000e^{-x^2-2y^2-z^2}) is -2000e^{-x^2-2y^2-z^2}x