What is (\partial)/(\partial x)(xye^{-1y}) ?

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

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(\partial)/(\partial x)(xye^{-1y})

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

e^{- y} y

Solution steps

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

Simplify

x y e^{- 1 \cdot y} : e^{- y} x y

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the common derivative:

\frac{\partial}{\partial x} (x) = 1

= e^{- y} y \cdot 1

Simplify

= e^{- y} y

x^{3}, 4 x

\frac{d}{d x} (x - arccos (x + 1))

y = (7 t - 4), (0, 3)

\frac{\partial}{\partial y} (x \cdot sin (y))

\frac{d}{d x} (sin (2 x) csc (\frac{x}{2}))

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