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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\int \frac{x ^{2} + 6 x + 2}{x ^{3} + 9 x ^{2} + 6 x + 9} d x

y^{^{'}} + 0.06 y = 6

n = 1 \sum \infty \frac{( n ! )}{n ^{n}}

y = 91

\int x^{2} (x + 1) d x

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