# Derivative of 1/(4x^2 + 3x - x)

1. Apr 30, 2004

### UrbanXrisis

what is the derivative of 1/(4x^2+3x-x)

I got 1/4x is that correct?

2. Apr 30, 2004

### Staff: Mentor

How did you get that?

3. Apr 30, 2004

### UrbanXrisis

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

4. Apr 30, 2004

### Ebolamonk3y

Wrong.

5. Apr 30, 2004

### Staff: Mentor

1/(a+b) does not equal 1/a + 1/b !!

Yikes!
If that were true, then this would follow:
$$\frac{1}{2} = \frac{1}{1+1} = \frac{1}{1} + \frac{1}{1} = 2$$

6. Apr 30, 2004

### UrbanXrisis

oh wow, what was I thinking??!?!? whooops. How would I solve this then?

7. Apr 30, 2004

### faust9

You could use the quotient rule, or simply rewrite the equation as $(4x^2+2x)^{-1}$ and use the regular chain rule.

PS: $\frac{1}{A+B+C}$ does not equal $\frac{1}{A}+\frac{1}{B}+\frac{1}{C}$ ; however, $\frac{A+B+C}{D}$ does equal $\frac{A}{D}+\frac{B}{D}+\frac{C}{D}$. See the difference? You cant simply split a denominator but you can split up a numerator. Use partial fractions to split the denominator.

 fixed my tex tags

Last edited: Apr 30, 2004