What is (\partial)/(\partial x)(2y^{1/2}x^{1/2}) ?

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

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(\partial)/(\partial x)(2y^{1/2}x^{1/2})

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 2 y^{\frac{1}{2}} \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

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

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

f (x) = \frac{10}{x}

x \to 2 lim (\frac{x ^{2}}{x ^{2} - 4})

\frac{d}{d x} (cos (x) d x)

\int - 4 sin (2 t - \frac{π}{2}) d t

\frac{d}{d x} (\frac{x tan ( x )}{x ^{2} + 1})

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