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 ?

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