# Differentiation of Quotients and Higher Derivatives

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?

ehild
Homework Helper
What is the first derivative of ##y=\frac{x^2}{x-2}##

ehild

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

Ray Vickson
Homework Helper
Dearly Missed
y=(x^2)-4x/(x-2)^2

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

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

HallsofIvy
Homework Helper
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
Do you mean "2x+ 9y= 3"? What are 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?
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.

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

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

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

ehild