Calculus Examples

$e^{x} + x^{e}$

Step 1

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

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

Step 2

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

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

Step 3

Differentiate using the Power Rule.

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Step 3.1

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

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

Step 3.2

Reorder terms.

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