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

Derive the function ln(ln(x)) with respect to x

Answer

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

Step-by-step explanation

Problem

$\frac{d}{dx}\left(\ln\left(\ln\left(x\right)\right)\right)$
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 $\displaystyle f'(x)=\frac{a'}{a}$

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

Unlock this step-by-step solution!

Answer

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

Main topic:

Differential calculus

Used formulas:

2. See formulas

Time to solve it:

~ 0.21 seconds