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/x1)
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)/(x1) )  I have a feeling that's the one, or
ln( x + 1/(x1) )
I will read it as ln ((x+1)/(x1))
then this can be changed to
ln(x+1)  ln(x1)
f ' (x) = 1/(x+1)  1/(x1)
= (x1  (x+1))/((x+1)(x1))
= 2/((x+1)(x1))
notice how important brackets are ?
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