differentiate and find the domain of ff(x) = ln ln ln x
- print Print
- list Cite
Expert Answers
mathsworkmusic
| Certified Educator
calendarEducator since 2012
write511 answers
starTop subjects are Math, Science, and Business
To differentiate `f(x) = ln(ln(ln(x)))` use the Chain Rule for differentiation of nested function.
The rule is that ` `if `f(x) = u(v(w(x)))` where `u, v` and `w` are functions
`f'(x) = u'(v(w(x)))v'(w(x))w'(x)`
Using the fact that `d/dx lnx = 1/x` we have that
` ``f'(x) = 1/ln(ln(x))1/ln(x)1/(x)` answer to first question
To find the domain of `f(x)` we proceed as follows
The domain of `x in (0,oo)`
So we need `ln(ln(ln(x)))` such that `ln(ln(x)) in (0,oo)`
`implies ln(x) in (1, oo)`
`implies x in (e^1,oo)` answer to second question
Related Questions
- `f(x) = x/(1 - ln(x - 1))` Differentiate f and find the domain of f.
- 1 Educator Answer
- `f(x) = sqrt(2 + ln(x))` Differentiate f and find the domain of f.
- 1 Educator Answer
- Differentiate ln(ln x)
- 1 Educator Answer
- How do i find the domain of the function f(x) = ln(cos(x))?
- 1 Educator Answer
- `f(x) = ln ln ln x` Differentiate f and find the domain of f.
- 1 Educator Answer