`f(x) = x/(1 - ln(x - 1))` Differentiate f and find the domain of f.
- print Print
- list Cite
Expert Answers
calendarEducator since 2015
write25 answers
starTop subjects are Math, Science, and Literature
This is a plot of `f(x) `, we will find the domain of `f(x) `, notice the missing values represented by circles in the plot.
Given `f(x) = x/(1-ln(x-1))` , we know that the denominator `1-ln(x-1)` cannot be zero. This means that ln(x-1)`!=1`. But when is ln(x-1)`=1`, that happens to be when `x-1=e=>x=1+e~~3.7 ` on the plot. Now `ln(x-1) ` can only take values of `x>1 ` since `x-1>0 ` for the `ln ` function to work. Thus, the domain of `f(x) ` is `x in (1,1+e) uu (1+e,+oo]`.
Turning over to the derivative of `f(x) `. Use the Quotient rule. To remind you it's `(f'*g-f*g')/(g^2) ` . Thus, `f'(x)=(1*(1-ln(x-1))-x*(-(1)/(x-1)))/((1-ln(x-1))^2) ` . Here we have used the fact that `(ln(x-1))'=(1)/(x-1) ` .
Going a bit further with simplification, `f'(x)=(1)/(1-ln(x-1))+(x)/((x-1)*(1-ln(x-1))^2) `
Related Questions
- `f(x) = sqrt(2 + ln(x))` Differentiate f and find the domain of f.
- 1 Educator Answer
- differentiate and find the domain of ff(x) = ln ln ln x
- 1 Educator Answer
- find the domain of f(x) = 1/sqrt(x-3)
- 1 Educator Answer
- How do i find the domain of the function f(x) = ln(cos(x))?
- 1 Educator Answer
- Find the inverse of f(x)=6x. What is the domain and range of f and f^-1.
- 1 Educator Answer