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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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