# Find the derivative of the following functions y=ln(lnx)

Tammy Todd

## Answered question

2021-10-10

Find the derivative of the following functions

$y=\mathrm{ln}\left(\mathrm{ln}x\right)$

### Answer & Explanation

Step 1

Given:

$y=\mathrm{ln}\left(\mathrm{ln}x\right)$

Step 2

Solution:

Derivative both sides with respect to x

$\frac{d}{dx}\left(y\right)=\frac{d}{dx}\left[\mathrm{ln}\left(\mathrm{ln}x\right)\right]$

$\frac{dy}{dx}=\frac{1}{\mathrm{ln}x}\frac{d}{dx}\left(\mathrm{ln}x\right)\text{}\text{}\text{}\Rightarrow [\frac{d}{dx}\left(\mathrm{ln}\left(x\right)\right)=\frac{1}{x}\left(\frac{d}{dx}x\right)]$

$\frac{dy}{dx}=\frac{1}{\mathrm{ln}x}\left(\frac{1}{x}\right)$

$\frac{dy}{dx}=\frac{1}{x\mathrm{ln}x}$

Step 3

Answer:

$\frac{dy}{dx}=\frac{1}{x\mathrm{ln}x}$

Answer is given below (on video)

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