What is (\partial)/(\partial x)(x^{1/2}y^{1/3}) ?

The answer to (\partial)/(\partial x)(x^{1/2}y^{1/3}) is (y^{1/3})/(2x^{1/2)}

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(\partial)/(\partial x)(x^{1/2}y^{1/3})

\frac{\partial}{\partial x} (x^{\frac{1}{2}} y^{\frac{1}{3}})

\frac{y ^{\frac{1}{3}}}{2 x ^{\frac{1}{2}}}

Solution steps

\frac{\partial}{\partial x} (x^{\frac{1}{2}} y^{\frac{1}{3}})

Treat

y

as a constant

Take the constant out:

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

= y^{\frac{1}{3}} \frac{\partial}{\partial x} (x^{\frac{1}{2}})

Apply the Power Rule:

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

= y^{\frac{1}{3}} \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

y^{\frac{1}{3}} \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{y ^{\frac{1}{3}}}{2 x ^{\frac{1}{2}}}

= \frac{y ^{\frac{1}{3}}}{2 x ^{\frac{1}{2}}}

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What is (\partial)/(\partial x)(x^{1/2}y^{1/3}) ?
The answer to (\partial)/(\partial x)(x^{1/2}y^{1/3}) is (y^{1/3})/(2x^{1/2)}