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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}})

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})

Popular Examples

integral of arccsc(x)

\int arccsc (x) d x

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n = 1 \sum \infty \frac{x ^{n}}{n + 5}

(\partial)/(\partial x)(7xy^4+2)

\frac{\partial}{\partial x} (7 x y^{4} + 2)

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\int \frac{1}{( x + 1 ) ( x ^{2} + 25 )} d x

integral of (x^{3/2}+8)^6sqrt(x)

\int (x^{\frac{3}{2}} + 8)^{6} x d x

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))