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

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

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

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

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

Solution steps

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

Apply the Power Rule:

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

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

Simplify

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

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

\int \frac{1}{( x - 1 ) ( x + 1 )} d x

f (x) = x^{3} - 2 x^{2} - 4 x - 6

\int (2 x + 5) e^{2 x + 5} d x

- \frac{9}{2} x^{2} + 3 x + 3

\frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} + 5})

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