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

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

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(\partial)/(\partial x)(xye^{x-3z})

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

y (e^{x - 3 z} + e^{x - 3 z} x)

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = e^{x - 3 z}

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

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

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

= y (1 \cdot e^{x - 3 z} + e^{x - 3 z} x)

Simplify

= y (e^{x - 3 z} + e^{x - 3 z} x)

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