Calculus Examples

$\frac{t^{3}}{3}$

Step 1

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

$\frac{1}{3} \frac{d}{d t} [t^{3}]$

Step 2

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

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

Step 3

Simplify terms.

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

Cancel the common factor.

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

Step 3.3.2

Divide $t^{2}$ by $1$ .

$t^{2}$