Calculus Examples

$s (t) = 13 t^{2}$ , $t = 2$

Step 1

Find the derivative.

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Step 1.1

Since $13$ is constant with respect to $t$ , the derivative of $13 t^{2}$ with respect to $t$ is $13 \frac{d}{d t} [t^{2}]$ .

$13 \frac{d}{d t} [t^{2}]$

Step 1.2

Differentiate using the Power Rule which states that $\frac{d}{d t} [t^{n}]$ is $n t^{n - 1}$ where $n = 2$ .

$13 (2 t)$

Step 1.3

Multiply $2$ by $13$ .

$26 t$

Step 2

Replace the variable $t$ with $2$ in the expression.

$s' (2) = 26 (2)$

Step 3

Multiply $26$ by $2$ .

$s' (2) = 52$