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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (8 y e^{5 x})

\int \frac{5 ^{- x}}{ln ( 5 )} d x

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

arcsin (sin (5 x))

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

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