Calculus Examples

$\ln (e^{x})$

Step 1

Use logarithm rules to move $x$ out of the exponent.

$\frac{d}{d x} [x \ln (e)]$

Step 2

The natural logarithm of $e$ is $1$ .

$\frac{d}{d x} [x \cdot 1]$

Step 3

Multiply $x$ by $1$ .

$\frac{d}{d x} [x]$

Step 4

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

$1$