What is (\partial)/(\partial x)(xye^{3y}) ?

The answer to (\partial)/(\partial x)(xye^{3y}) is e^{3y}y

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(\partial)/(\partial x)(xye^{3y})

\frac{\partial}{\partial x} (x y e^{3 y})

e^{3 y} y

Solution steps

\frac{\partial}{\partial x} (x y e^{3 y})

Treat

y

as a constant

Take the constant out:

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

= y e^{3 y} \frac{\partial}{\partial x} (x)

Apply the common derivative:

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

= y e^{3 y} \cdot 1

Simplify

= e^{3 y} y

What is (\partial)/(\partial x)(xye^{3y}) ?
The answer to (\partial)/(\partial x)(xye^{3y}) is e^{3y}y