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

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

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

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

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

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

Solution steps

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

Simplify

e^{- \frac{x ^{2}}{2} - \frac{y ^{2}}{2}} : e^{\frac{- x ^{2} - y ^{2}}{2}}

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

Apply the chain rule:

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

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

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

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

e^{x}

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

- 5 sin (3 t)

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

\int - e^{x} x d x

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