How do you differentiate $y = \sqrt{x + 1} - ln (1 + \sqrt{x + 1})$ $y=sqrt(x+1)-ln(1+sqrt(x+1))$ ?

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Answer 1 · 2017-12-11T17:52:42

$y'=(sqrt(x+1)-1)/(2x)$

$y=sqrt(x+1)-ln(1+sqrt(x+1))$

$y'=1/[2sqrt(x+1)]-(1/[2sqrt(x+1)])/(1+sqrt(x+1)$

= $1/[2sqrt(x+1)]*(1-1/[sqrt(x+1)+1])$

= $1/[2sqrt(x+1)]*(sqrt(x+1)/[sqrt(x+1)+1])$

= $1/2*1/[sqrt(x+1)+1]$

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

How do you differentiate y=sqrt(x+1)-ln(1+sqrt(x+1))y=√x+1−ln(1+√x+1)y=sqrt(x+1)-ln(1+sqrt(x+1))?