What is (\partial)/(\partial x)(2sqrt(xy)-ye^{y/z}) ?

The answer to (\partial)/(\partial x)(2sqrt(xy)-ye^{y/z}) is (y/x)^{1/2}

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(\partial)/(\partial x)(2sqrt(xy)-ye^{y/z})

\frac{\partial}{\partial x} (2 x y - y e^{\frac{y}{z}})

(\frac{y}{x})^{\frac{1}{2}}

Solution steps

\frac{\partial}{\partial x} (2 x y - y e^{\frac{y}{z}})

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 x y) - \frac{\partial}{\partial x} (y e^{\frac{y}{z}})

\frac{\partial}{\partial x} (2 x y) = (\frac{y}{x})^{\frac{1}{2}}

\frac{\partial}{\partial x} (y e^{\frac{y}{z}}) = 0

= (\frac{y}{x})^{\frac{1}{2}} - 0

Simplify

= (\frac{y}{x})^{\frac{1}{2}}

What is (\partial)/(\partial x)(2sqrt(xy)-ye^{y/z}) ?
The answer to (\partial)/(\partial x)(2sqrt(xy)-ye^{y/z}) is (y/x)^{1/2}