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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{x - y}

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

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

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

= y (1 \cdot e^{x - y} + e^{x - y} x)

Simplify

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

\frac{7}{x ^{6}}

\frac{d}{d x} (- \frac{1}{( x + 1 ) ^{2}})

3 (1 + x^{2}) \frac{d y}{d x} = 2 x y^{4}

\int \frac{1}{4 - 9 x ^{2}} d x

x \to 3 lim (6 - 2 x)

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