Calculus Examples

$\ln (e^{3 x})$

Step 1

Use logarithm rules to move $3 x$ out of the exponent.

$\frac{d}{d x} [3 x \ln (e)]$

Step 2

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

$\frac{d}{d x} [3 x \cdot 1]$

Step 3

Multiply $3$ by $1$ .

$\frac{d}{d x} [3 x]$

Step 4

Since $3$ is constant with respect to $x$ , the derivative of $3 x$ with respect to $x$ is $3 \frac{d}{d x} [x]$ .

$3 \frac{d}{d x} [x]$

Step 5

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

$3 \cdot 1$

Step 6

Multiply $3$ by $1$ .

$3$