so what do you all finally say isnt the answer 1/x and whats wrong with my approach

 

and anyone who says chain rule is wrong

 

it is right here as x can never take a value 0 so need not to split and you forgot that |x| in that denominator it cancels |x| in the numerator and we get the answer even if you do it by taking it case by case you will end up with the same answer!!!

 

answer is 1/x