# Thread: Differentiate the following by either, Product Rule, Function of a Function or

1. ## Differentiate the following by either, Product Rule, Function of a Function or

Differentiate the following by either, Product Rule, Function of a Function or Quotient Rule

1. $\displaystyle x\sqrt{(x+1)}$ : I Think this one is the Product Rule

2. $\displaystyle (x^2 - 8)^3$ : Guessing this is Function of a Function

3. $\displaystyle \frac{x}{(x+1}$ : : And this one I believe is Quotient Rule

as to how you work them out I wouldn't have a clue lol

Thanks for any help

2. Originally Posted by Maths_noob
Differentiate the following by either, Product Rule, Function of a Function or Quotient Rule

1. $\displaystyle x\sqrt{(x+1)}$ : I Think this one is the Product Rule

2. $\displaystyle (x^2 - 8)^3$ : Guessing this is Function of a Function

3. $\displaystyle \frac{x}{(x+1}$ : : And this one I believe is Quotient Rule

as to how you work them out I wouldn't have a clue lol

Thanks for any help
get a clue, then ...

Karl's Calculus Tutor - Box 4.4x: Rules for Derivatives

specifically rules 5, 6, and 7

3. Thanks for the link,
Ive got 20 of these to do in total,
Is there chance someone could do these three for me?

As I'm sturggling failing to understand how everything is being substituted in on the equations currently.

Thanks

4. $\displaystyle y = x\sqrt{x+1}$

$\displaystyle y = x(x+1)^{\frac{1}{2}}$

$\displaystyle y' = x \cdot \frac{1}{2}(x+1)^{-\frac{1}{2}} + (x+1)^{\frac{1}{2}} \cdot 1$

$\displaystyle y' = \frac{x}{2\sqrt{x+1}} + \sqrt{x+1} = \frac{x}{2\sqrt{x+1}} + \frac{2(x+1)}{2\sqrt{x+1}} = \frac{3x+2}{2\sqrt{x+1}}$

$\displaystyle y = (x^2-8)^3$

$\displaystyle y' = 3(x^2-8)^2 \cdot 2x$

$\displaystyle y' = 6x(x^2-8)^2$

$\displaystyle y = \frac{x}{x+1}$

$\displaystyle y' = \frac{(x+1) \cdot 1 - x \cdot 1}{(x+1)^2}$

$\displaystyle y' = \frac{1}{(x+1)^2}$