What is the derivative of e^{-x^2-y^2} ?

The derivative of e^{-x^2-y^2} is e^{-x^2-y^2}(-2x-2y(dy)/(dx))

What is the first derivative of e^{-x^2-y^2} ?

The first derivative of e^{-x^2-y^2} is e^{-x^2-y^2}(-2x-2y(dy)/(dx))

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

What is the derivative of e^{-x^2-y^2} ?
The derivative of e^{-x^2-y^2} is e^{-x^2-y^2}(-2x-2y(dy)/(dx))
What is the first derivative of e^{-x^2-y^2} ?
The first derivative of e^{-x^2-y^2} is e^{-x^2-y^2}(-2x-2y(dy)/(dx))