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

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

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

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

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

Solution steps

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

Apply the Power Rule:

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

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

Simplify

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

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

\frac{d}{d x} (\frac{1}{3} tan^{3} (\frac{x}{2}) - tan (\frac{x}{2}))

\frac{d}{d x} (sec^{4} (2) x^{2})

\frac{d}{d x} (n x^{n})

\frac{2 x ^{2} + 8 x + 4}{x}

\frac{d}{d x} (\frac{- cos ( x ) - 1}{x ^{3} + x ^{2}})

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