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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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