Differentiation of Quotients and Higher Derivatives

1. Sep 19, 2014

Aichuk

1) The line 2x+9=3 meets curve xy+y+2=0 at the points P and Q. Calculate the gradient of the curve at P and Q

2)Given that $y=(x^2)/(x-2)$, find
a) $(d^2)y/dx^2$ in its simplest form
b)ther range of value for which $dy/dx$ and $(d^2)y/dx^2$ are positive.

I can't figure out either of the sums. For the first one I got the answer -1/11 & -44/81 (even though the answer page showed 1/2 and 4/81) and the second I couldn't do. Can anyone do them step by step?

2. Sep 19, 2014

ehild

What is the first derivative of $y=\frac{x^2}{x-2}$

ehild

3. Sep 19, 2014

Aichuk

y=(x^2)-4x/(x-2)^2

4. Sep 19, 2014

Ray Vickson

How did you get
$$\frac{d}{dx} \frac{x^2}{x-2} = x^2 - \frac{4x}{(x-1)^2} ?$$
This is obviously wrong.

5. Sep 19, 2014

Aichuk

No, i got $y= \frac{x^2-4x}{(x-2)^2}$

6. Sep 19, 2014

HallsofIvy

Staff Emeritus
Do you mean "2x+ 9y= 3"? What are P and Q?

As Ray Vickson pointed out, you have written the first derivative incorrectly- although you may have calculated it correctly. You have the parentheses in the wrong place and you have the denominator wrong.

7. Sep 19, 2014

Aichuk

Sorry for that, I suck at typing equations on computer.

8. Sep 19, 2014

Staff: Mentor

9. Sep 19, 2014

ehild

Did you mean $\frac{dy}{dx}$?

ehild