See explanation.

If you mean: ##sqrt(x)+1/sqrt(x)##

Derivative is given by:

##1/(2sqrt(x)) – 1/(2sqrt(x^3))= (x-1) / (2x^(3/2))##

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If you mean: ##sqrt(x+1)/sqrt(x)##

Derivative is given by:

##( sqrt(x) / (2sqrt(x+1)) – (sqrt(x+1)) / (2sqrt(2)) ) / x##

##implies sqrt(x) / (2xsqrt(x+1)) – (sqrt(x+1)) / (2xsqrt(2)) =- 1/ ( 2x^(3/2)sqrt(x+1) ) ##

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