What is (\partial)/(\partial x)(e^{-1/2 xy}) ?

The answer to (\partial)/(\partial x)(e^{-1/2 xy}) is -(e^{-(xy)/2}y)/(2)

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(\partial)/(\partial x)(e^{-1/2 xy})

\frac{\partial}{\partial x} (e^{- \frac{1}{2} x y})

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

Solution steps

\frac{\partial}{\partial x} (e^{- \frac{1}{2} x y})

Simplify

e^{- \frac{1}{2} x y} : e^{- \frac{x y}{2}}

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int - 2 x + 6 d x

y^{^{'}} + \frac{1}{x + 7} y = x^{- 2}, y (1) = 4

\frac{\partial}{\partial x} (x cos (x) cos (y))

x \to 2 lim (\frac{3 x ^{2} - 5 x - 2}{2 x - 1})

What is (\partial)/(\partial x)(e^{-1/2 xy}) ?
The answer to (\partial)/(\partial x)(e^{-1/2 xy}) is -(e^{-(xy)/2}y)/(2)