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

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

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

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

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

Solution steps

\frac{\partial}{\partial x} (x^{\frac{2}{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{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}}}

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

\frac{d}{d x} ((2 x^{4} - 6 x^{2} + 5)^{2})

- y + y^{^{'}} - y = e^{x} cos (x)

\frac{d ^{2} y}{d x ^{2}}, x y + 7 ey (x) = 7 e

f (x) = tan (x) - 1 sec (x)

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