# How do I find the derivative of f(x)=ln(x^2)?

Mar 2, 2018

Using Chain Rule, the answer is $\frac{2}{x}$

#### Explanation:

The Chain Rule is:

$\frac{\mathrm{df}}{\mathrm{du}} \cdot \frac{\mathrm{du}}{\mathrm{dx}}$

where $f$ is the general function

where $u$ is the function within the function

Here, $f = \ln \left(u\right)$ and $u = {x}^{2}$

Now, we can substitute:

$\frac{d}{\mathrm{du}} \ln \left(u\right) \cdot \frac{d}{\mathrm{dx}} {x}^{2}$

Find the respective derivatives:

$= \frac{1}{u} \cdot 2 x$

Since $u = {x}^{2}$, we can substitute:

$\frac{1}{x} ^ 2 \cdot 2 x$

$x$ and $x$ cancel out:

$\frac{1}{x} \cdot 2$

$= \frac{2}{x}$