Calculus Examples

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

Since $\frac{1}{2}$ is constant with respect to $y$ , the derivative of $\frac{y^{3}}{2}$ with respect to $y$ is $\frac{1}{2} \frac{d}{d y} [y^{3}]$ .

$\frac{1}{2} \frac{d}{d y} [y^{3}]$

Differentiate using the Power Rule which states that $\frac{d}{d y} [y^{n}]$ is $n y^{n - 1}$ where $n = 3$ .

$\frac{1}{2} (3 y^{2})$

Combine fractions.

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Combine $3$ and $\frac{1}{2}$ .

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

Combine $\frac{3}{2}$ and $y^{2}$ .

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