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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

n = 0 \sum \infty n^{2} x^{n}

\int (3 x + 2)^{4} d x

\frac{d}{d x} (e^{2 x} sin (6 x))

\frac{d}{d x} (\frac{4 x - 12}{( x - 2 ) ^{2}})

x \to 3 - lim (3 - x)

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