What is (\partial)/(\partial x)(xe^y-3yz) ?

The answer to (\partial)/(\partial x)(xe^y-3yz) is e^y

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(\partial)/(\partial x)(xe^y-3yz)

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

e^{y}

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial x} (3 yz) = 0

= e^{y} - 0

Simplify

= e^{y}

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What is (\partial)/(\partial x)(xe^y-3yz) ?
The answer to (\partial)/(\partial x)(xe^y-3yz) is e^y