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

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

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(\partial)/(\partial x)(2sqrt(x)y-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}}}

4 e^{x} + x

\int_{0}^{9} \frac{1}{81 + t ^{2}} d t

x^{8}

\frac{d}{d x} (x (x - 2)^{2})

\frac{1}{s ^{2} + 4 s + 20}

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