How to differentiate this?

Question

#y=ln(sqrt(x+1))#

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Answer 1 · 2018-03-22T17:26:15

#(dy)/(dx) = 1/(2x+2)#

we know #d/dx( ln f(x)) = ( f'(x) ) / ( f(x) ) #

#=> d/dx ( lnsqrt(x+1) ) = d/dx( 1/2 ln (x+1) ) #

#=> 1/2( d/dx(1+x) )/(x+1) #

#=> 1/2 ( 1/(x+1) ) #

#=> 1/(2x+2) #