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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\int \frac{u}{u ^{2} + 1} d u

x \to 0 lim (\frac{ln ( \frac{1 + x}{1 - x} ) - 2 x}{x - sin ( x )})

\int x x^{4} + 1 d x

f (x) = 6 x - x^{2}, at x = 0

f (t) = 80 t + t^{2} - \frac{1}{48} t^{3}

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