Calculus Problem: Find Derivative of f(x)= (x+1)/(x+2)(3x^2 + 6x)

[Taturana]

Homework Statement

Find the derivative of:

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

Homework Equations

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

 

[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

 

[Taturana]

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

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?

 

[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.

 

[rock.freak667]

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?

You can do it however you wish!

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.

Like hunt_mat shows you.

 

[Taturana]

Ok, thank you all