Calculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Multiply $x^{2}$ by $1$ .

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

Step 4

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 2$ .

$2 x$