# Find the double derivate of

1. Dec 19, 2012

### f22archrer

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

f(x) = (-5x^2+3x) / (2x^2-5)

2. Relevant equations

f 'x)=
(-6x^2+50x-15) / ( 2x^2-5)^2

3. The attempt at a solution
f ''x= ?

2. Dec 19, 2012

### Staff: Mentor

Can you please show all the steps you used to take the first derivative?

3. Dec 19, 2012

### f22archrer

f'(x) = (2x^2 -5)((-10x+3) -(-5x^2+3x)4x) / 2x^2-5
= -20x^3 +6x^2+50x-15+20x^3-12x^2 / (2x^ - 5)^2
= -6x^2 +50x-15 / (2x^2 - 5)^2

4. Dec 19, 2012

### Staff: Mentor

Thanks, that makes it much easier to check. I think it's correct so far, now just apply the quotient rule one more time to get the second derivative...

5. Dec 19, 2012

### lurflurf

Either use the quotient rule on your first derivative (which is right), or use the second derivative quotient rule, or use the product rule.

$$\left( \dfrac{u}{v} \right) ^{\prime \prime}=\dfrac{u^{\prime \prime} v^2-2u^\prime v v^\prime+2u (v^\prime)^2-u v^{\prime \prime}}{v^3}$$

6. Dec 19, 2012

### SammyS

Staff Emeritus
It helps to use sufficient number of parentheses. A little spacing can also help.