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

• May 25th 2009, 05:25 AM
Maths_noob
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. $x\sqrt{(x+1)}$ : I Think this one is the Product Rule

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

3. $\frac{x}{(x+1}$ : : 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
• May 25th 2009, 06:27 AM
skeeter
Quote:

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

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

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

3. $\frac{x}{(x+1}$ : : 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
• May 25th 2009, 09:19 AM
Maths_noob
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
• May 25th 2009, 09:39 AM
skeeter
$y = x\sqrt{x+1}$

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

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

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

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

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

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

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

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

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