Posted by **cathy** on Tuesday, October 30, 2012 at 1:16am.

how would i find the derivative of these?

f(x)=ln((√x)+1)

and

f(x)=ln(x+1/x-1)

thank u!!

- calc -
**Reiny**, Tuesday, October 30, 2012 at 9:31am
first one:

remember that √x = x^(1/2)

f ' (x) = 1/(√x + 1) ( (1/2)x^(-1/2)

= 1/( 2x^(1/2) (√x)(√x + 1)

= 1/( 2√x(√x + 1) or 1/(2(x+√x)

2nd:

not clear if you meant

ln( x + 1/x - 1) --- the way you typed it , or

ln( (x+1)/(x-1) ) --- I have a feeling that's the one, or

ln( x + 1/(x-1) )

I will read it as ln ((x+1)/(x-1))

then this can be changed to

ln(x+1) - ln(x-1)

f ' (x) = 1/(x+1) - 1/(x-1)

= (x-1 - (x+1))/((x+1)(x-1))

= -2/((x+1)(x-1))

notice how important brackets are ?

## Answer This Question

## Related Questions

- Math - Find an equation of the line that bisects the obtuse angles formed by the...
- Calculus - How would I find the second derivative if f(x)= √(x^3+2) using ...
- Calculus - y=(√x)/((√x)+1) Find the concavity and point of ...
- Math - Could I please get some help for these 3 questions, apologies for asking ...
- 8th grade algebra - Can you check my answers? 1. 3√20/√4 = 3√(...
- Algebra - How would i complete these problems? 1. (√6mn)^5 2. ^3√16x...
- Algebra 2 Answer Check - Simplify by rationalizing each denominator. 1. 2/√...
- CALC 1 - Suppose that h is a function with h'(x) = xe^x. Find all intervals ...
- maths - I will be thankfull to you if you help me to solve the below problem: 6...
- calc - derivative of (x^3/6)+(1/2x)? i got (x^2/2)-(1/2x^2) is that correct? and...

More Related Questions