Posted by sh on Tuesday, October 20, 2009 at 10:53pm.
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.

Calculus  Reiny, Tuesday, October 20, 2009 at 10:59pm
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))

Calculus  sh, Tuesday, October 20, 2009 at 11:03pm
What did you do to get the first line?

Calculus  Reiny, Tuesday, October 20, 2009 at 11:07pm
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.

Calculus  sh, Tuesday, October 20, 2009 at 11:08pm
Oh, I haven't learnt the quotient rule, only the power rule, thanks.

Calculus  Reiny, Tuesday, October 20, 2009 at 11:35pm
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.

Calculus  sh, Tuesday, October 20, 2009 at 11:44pm
The back of the textbook just left it as y'= (1/2)x(1/2)  (1/2)x^(3/2)
Thanks! :)
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