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)
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))
notice how important brackets are ?
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