What is (\partial)/(\partial y)(xye^y) ?

The answer to (\partial)/(\partial y)(xye^y) is x(e^y+e^yy)

(\partial)/(\partial y)(xye^y)

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = y, g = e^{y}

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

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

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

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

Simplify

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

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\int \frac{5}{2 x - 2} d x

x \to 1 + lim (\frac{x}{ln ( x )})

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