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}

= (x-1)/(2x^(3/2))

Just noticed that in my intial reply I had x+1 instead of x-1 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! :)

## Answer this Question

## Related Questions

- Math - Find an equation of the line that bisects the obtuse angles formed by the...
- maths - I will be thankfull to you if you help me to solve the below problem: 6...
- Algebra - How would i complete these problems? 1. (√6mn)^5 2. ^3√16x...
- Algebra - Simplify the expressions and solve the equations 1. 2√3 - √...
- Algebra Work Check - 1. 5√6 * 1/6√216 5/6 * √1296 5/6 * √...
- Algebra 2 Answer Check - Simplify by rationalizing each denominator. 1. 2/√...
- Math help Ms. Sue please - 1. What is the simplified form of the expression? 7m^...
- algebra 1 - alright i have a few questions if its ok..? Simplify: 1. -2√(...
- Algebra 2 - Can someone help me with this radical expression please? The problem...
- Precalculus - Determine the exact value of cos 465 degrees a) √3 + √...

More Related Questions