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

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

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

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

- e^{- x y} y

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= e^{- x y} (- y)

Simplify

= - e^{- x y} y

x \to + 2 + lim (x^{2})

\frac{d}{d x} (z arctan (\frac{y}{x}))

\frac{e ^{x}}{e ^{x} + 1}

y^{^{''}} + 5 y = - 180 x^{2} e^{5 x}

y^{^{'}} = \frac{( 4 t + y )}{( 4 y - t )}

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