Calculus Examples

$k (r) = e^{r} + r^{e}$

Step 1

By the Sum Rule, the derivative of $e^{r} + r^{e}$ with respect to $r$ is $\frac{d}{d r} [e^{r}] + \frac{d}{d r} [r^{e}]$ .

$\frac{d}{d r} [e^{r}] + \frac{d}{d r} [r^{e}]$

Step 2

Differentiate using the Exponential Rule which states that $\frac{d}{d r} [a^{r}]$ is $a^{r} \ln (a)$ where $a$ = $e$ .

$e^{r} + \frac{d}{d r} [r^{e}]$

Step 3

Differentiate using the Power Rule.

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Step 3.1

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

$e^{r} + e r^{e - 1}$

Step 3.2

Reorder terms.

$e r^{e - 1} + e^{r}$