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Find the derivative of $\ln\left(\ln\left(x\right)\right)$

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Final Answer

$\frac{1}{\ln\left(x\right)}\frac{1}{x}$
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Step-by-step Solution

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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 $\displaystyle f'(x)=\frac{a'}{a}$

$\frac{1}{\ln\left(x\right)}\frac{d}{dx}\left(\ln\left(x\right)\right)$
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 $\displaystyle f'(x)=\frac{a'}{a}$

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

Final Answer

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

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind derivative of lnlnx using the product ruleFind derivative of lnlnx using the quotient ruleFind derivative of lnlnx using logarithmic differentiation

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Function Plot

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

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1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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