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Popular >

derivative of e^{-(x^2+y^2})

Solution

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

Solution

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})})

Simplify

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

= \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})

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Frequently Asked Questions (FAQ)

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))