Calculus Examples

$\ln (e^{2 x})$

Step 1

Use logarithm rules to move $2 x$ out of the exponent.

$\frac{d}{d x} [2 x \ln (e)]$

Step 2

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

$\frac{d}{d x} [2 x \cdot 1]$

Step 3

Multiply $2$ by $1$ .

$\frac{d}{d x} [2 x]$

Step 4

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

$2 \frac{d}{d x} [x]$

Step 5

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

$2 \cdot 1$

Step 6

Multiply $2$ by $1$ .

$2$