What is (\partial)/(\partial x)(x*e^{x-y-z}) ?

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

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(\partial)/(\partial x)(x*e^{x-y-z})

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

e^{x - y - z} + e^{x - y - z} x

Solution steps

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

Treat

y, z

as constants

Apply the Product Rule:

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

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

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

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

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

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

Simplify

= e^{x - y - z} + e^{x - y - z} x

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