What is the first d/(dy)((y^3)/3) ?

The first d/(dy)((y^3)/3) is y^2

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d/(dy)((y^3)/3)

\frac{d}{d y} (\frac{y ^{3}}{3})

y^{2}

Solution steps

\frac{d}{d y} (\frac{y ^{3}}{3})

Take the constant out:

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

= \frac{1}{3} \frac{d}{d y} (y^{3})

Apply the Power Rule:

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

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

Simplify

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

= y^{2}