Calculus
posted by sh on .
Differentiate the following function:
y= [x+1]/√x
I tried
y=[x+1]/x^(1/2)
y' =1/2√x
y'=2√x
Thanks in advance.

OH MY!
my first line after the quotient rule is
dy/dx = (√x  (1/2)x(1/2)(x+1))/x
which reduces to (x+1)/(2x^(3/2)) 
What did you do to get the first line?

As I said, I used the quotient rule.
Judging by the type of question you are differentiating, you must know that.
alternate way,
change your question to
y = (x+1)(x^(1/2)) and use the product rule.
same result of course. 
Oh, I haven't learnt the quotient rule, only the power rule, thanks.

ok then try this
y = (x+1)/√x
= x/√x + 1/√x
= x^(1/2) + x^(1/2)
so dy/dx = (1/2)x(1/2)  (1/2)x^(3/2)
= (1/2)x^(3/2)[x  1}
= (x1)/(2x^(3/2))
Just noticed that in my intial reply I had x+1 instead of x1 in the numerator.
This last result is the correct one. 
The back of the textbook just left it as y'= (1/2)x(1/2)  (1/2)x^(3/2)
Thanks! :)