# Step-by-step Solution

## Derive the function $\ln\left(\ln\left(x\right)\right)$ with respect to x

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### Videos

$\frac{1}{x\ln\left(x\right)}$

## Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(\ln\left(\ln\left(x\right)\right)\right)$
1

The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$

$\frac{1}{\ln\left(x\right)}\cdot\frac{d}{dx}\left(\ln\left(x\right)\right)$
2

The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$

$\frac{1}{x}\cdot\frac{1}{\ln\left(x\right)}$

$\frac{1}{x\ln\left(x\right)}$
$\frac{d}{dx}\left(\ln\left(\ln\left(x\right)\right)\right)$

### Main topic:

Differential calculus

~ 0.43 seconds