# Thread: one more derivative -using quotient

1. ## one more derivative -using quotient

find the derivative of

x^2
-----------
root (x+1)

x(3x+4)
-------------
2(x+1)^3/2

using quotient rule, i got as far as:
(2x)(x+1)^1/2 - (x^2)1/2(x+1)^1/2
--------------------------------------------
x+1

not quite sure what to do after...do i factor out?
Thanks!

2. Multiply and divide 2(x+1)^1/2 to the numerator and the denominator and simplify.

3. Originally Posted by calculus0
find the derivative of

x^2
-----------
root (x+1)

x(3x+4)
-------------
2(x+1)^3/2

using quotient rule, i got as far as:
(2x)(x+1)^1/2 - (x^2)1/2(x+1)^1/2
--------------------------------------------
x+1

not quite sure what to do after...do i factor out?
Thanks!
[tex]Here you have $\displaystyle y = \frac{u}{v}$

so $\displaystyle \frac{dy}{dx} = \frac{v\,\frac{du}{dx} - u\,\frac{dv}{dx}}{v^2}$.

Which part are you having trouble with?

4. so if i multiply top and bottom do i get:

4x(x+1)3/2 - x^2
------------------------
2(x+1)^2

? something is still wrong.. i think im getting closer, but still not the final answer

5. Originally Posted by calculus0
find the derivative of

x^2
-----------
root (x+1)

x(3x+4)
-------------
2(x+1)^3/2

using quotient rule, i got as far as:
(2x)(x+1)^1/2 - (x^2)1/2(x+1)^1/2
--------------------------------------------
x+1
That second term should be (x^2)(1/2)(x+1)^-1/2

not quite sure what to do after...do i factor out?
Thanks!
You might find it easier to write this as x^2(x+1)^(-1/2) and use the product rule.

6. Originally Posted by calculus0
so if i multiply top and bottom do i get:

4x(x+1)3/2 - x^2
------------------------
2(x+1)^2

? something is still wrong.. i think im getting closer, but still not the final answer
(x+1)^1/2*(x+1)^1/2 = .............?

(x+1)*(x+1)^1/2 = ...........?