Calculus Examples

$\frac{t^{4}}{4}$

Step 1

Since $\frac{1}{4}$ is constant with respect to $t$ , the derivative of $\frac{t^{4}}{4}$ with respect to $t$ is $\frac{1}{4} \frac{d}{d t} [t^{4}]$ .

$\frac{1}{4} \frac{d}{d t} [t^{4}]$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d t} [t^{n}]$ is $n t^{n - 1}$ where $n = 4$ .

$\frac{1}{4} (4 t^{3})$

Step 3

Simplify terms.

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Step 3.1

Combine $4$ and $\frac{1}{4}$ .

$\frac{4}{4} t^{3}$

Step 3.2

Combine $\frac{4}{4}$ and $t^{3}$ .

$\frac{4 t^{3}}{4}$

Step 3.3

Cancel the common factor of $4$ .

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Step 3.3.1

Cancel the common factor.

$\frac{4 t^{3}}{4}$

Step 3.3.2

Divide $t^{3}$ by $1$ .

$t^{3}$