Find the derivative of the question

1. Mar 16, 2013

ASidd

1. The problem statement, all variables and given/known data

(9x-8)/ 2(sqrt(3x-4))

2. Relevant equations
Vu'-Uv'/v^2

i.e. quotient rule

3. The attempt at a solution
I get
V=2(sqrt(3x-4) u=9x-8
V'=3((3x-4)^-1.5) u'=9

When I put this into the equation and solve I get
9x-8(sqrt(3x-4))/6x-8

2. Mar 16, 2013

HallsofIvy

Staff Emeritus
With v= 2sqrt(3x- 4)= 2(3x- 4)^1/2, v'= 3(3x- 4)^-(1/2)= 3(3x- 4)^(.5-1)= 3(3x- 4)^-.5, not "-1.5". That's your basic error.

So u'v- uv'= 9(2(3x-4)^1/2)- (9x- 8)(3(3x-4)^-1/2
To combine those two square roots, use the fact that (3x-4)^1/2= (3x- 4)(3x-4)^-1/2 so we can factor (3x- 4)^-1/2 out: (3x-4)^-1/2(18(3x- 4)- 3(9x- 8))= (3x-4)^-1/2(54x- 72- 27x+ 24)= (3x- 4)^-1/2(27x- 48)= (3x- 4)^-1/2(3)(9x- 16).

Can you finish?
By the way, with that power in the denominator, so you will need to use the chain rule, anyway, it might be simpler to write the function as (1/2)(9x- 8)(3x-4)^-1/2 and use the product rule rather than the quotient rule.

3. Mar 16, 2013

HomogenousCow

Writing fractions without LaTex should be punishable by death