# Calculus problem

1. Aug 23, 2010

### Taturana

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

Find the derivative of:

$$f(x) = \frac{x+1}{x+2} (3x^2 + 6x)$$

2. Relevant equations
3. The attempt at a solution

I tried but I don't know what rules should I apply here, so it's a waste of database space post here my wrong solution...

(Should I first to the derivative of the fraction and then to the product rule using the derivative of the fraction and the other thing in the parenthesis?)

Thank you,
Rafael Andreatta

2. Aug 23, 2010

### rock.freak667

Use the product rule and then the quotient rule.

$$f(x) = \frac{x+1}{x+2} (3x^2 + 6x)$$

u=(x+1)/(x+2) du/dx = quotient rule.

v=3x2 + 6x

3. Aug 23, 2010

### Taturana

So I first use the product rule for $$(x+1)(3x^2 + 6x)$$ and then the quotient rule between the result of the product rule and the (x+2)?

Why can't I do first eh quotient rule and then the product rule?

4. Aug 23, 2010

### hunt_mat

You can, it's your choice what you use. I might write:
$$\frac{x+1}{x+2} (3x^2 + 6x)=\frac{3x(x+1)(x+2)}{x+2}=3x^{2}+3x$$
Then I don't need to apply the product rule or the quotient rule.

5. Aug 23, 2010

### rock.freak667

You can do it however you wish!

Like hunt_mat shows you.

6. Aug 23, 2010

### Taturana

Ok, thank you all