Calculus Examples

$r t^{r - 1}$

Step 1

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

$r \frac{d}{d t} [t^{r - 1}]$

Step 2

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

$r ((r - 1) t^{r - 1 - 1})$

Step 3

Simplify the expression.

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Step 3.1

Subtract $1$ from $- 1$ .

$r ((r - 1) t^{r - 2})$

Step 3.2

Reorder the factors of $r ((r - 1) t^{r - 2})$ .

$t^{r - 2} r (r - 1)$