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

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

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(\partial)/(\partial x)(ye^{x/z})

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

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

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

y e^{\frac{x}{z}} \frac{1}{z} : \frac{e ^{\frac{x}{z}} y}{z}

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

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