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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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