Calculus Examples

y = \ln (e^{x^{2}})

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

Step 1

Use logarithm rules to move

x^{2}

$x^{2}$ out of the exponent.

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

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

Step 2

The natural logarithm of

e

$e$ is

1

$1$ .

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

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

Step 3

Multiply

x^{2}

$x^{2}$ by

1

$1$ .

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

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

Step 4

Differentiate using the Power Rule which states that

\frac{d}{d x} [x^{n}]

$\frac{d}{d x} [x^{n}]$ is

n x^{n - 1}

$n x^{n - 1}$ where

n = 2

$n = 2$ .

2 x

$2 x$

y = \ln (e^{x^{2}})

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

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