What is (\partial)/(\partial x)(xe^{(y/z)}) ?

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

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(\partial)/(\partial x)(xe^{(y/z)})

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

e^{\frac{y}{z}}

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the common derivative:

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

= e^{\frac{y}{z}} \cdot 1

Simplify

= e^{\frac{y}{z}}

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

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