1. ## Differentiation

Find the slope of the curve y= (x)/(x^2+1) at the origin. Find the equation of the tangent and of the normal at the origin.

Is this how I find y:
y= (0)/(0^2+1)
=0
where I have place x=0

I cannot attempt this as I have no idea where to start this question. I think I do not understand this question. Thanks.

2. Originally Posted by Awsom Guy
Find the slope of the curve y= (x)/(x^2+1) at the origin. Find the equation of the tangent and of the normal at the origin.

Is this how I find y:
y= (0)/(0^2+1)
=0
where I have place x=0

I cannot attempt this as I have no idea where to start this question. I think I do not understand this question. Thanks.
You should know how to find the equation of a tangent.

Find the derivative, evaluate it at x = 0. Substitute into y = mx + c to find the y intercept.

For the normal, remember that $m_1m_2 = -1$ for perpendicular lines.

3. If this is the derivation: (x^2-1)/(x^2+1)^2
then if I nake x=0 and do this:
(0-1)/(0^2+1)(0^2+1)
=-1/1
=-1
Does this find the y co-ordinate or the gradient.

4. Originally Posted by Awsom Guy
If this is the derivation: (x^2-1)/(x^2+1)^2
then if I nake x=0 and do this:
(0-1)/(0^2+1)(0^2+1)
=-1/1
=-1
Does this find the y co-ordinate or the gradient.
Close, but the derivative is actually $\frac{1 - x^2}{(x^2 + 1)^2}$ (found using the Quotient Rule).

After you substitute $x = 0$, you have the GRADIENT of the tangent.

5. Now how do I place that onto the y=mx+b formula, the gradient is 1. So it is y=1x+b. How do i find y, do I make y=0.
Thanks

6. Originally Posted by Awsom Guy
Now how do I place that onto the y=mx+b formula, the gradient is 1. So it is y=1x+b. How do i find y, do I make y=0.
Thanks
You have already found that the point $(x, y) = (0, 0)$ lies on the curve. If the gradient is $1$, then $m = 1$.

Put these three values into the equation $y = mx + c$ and find $c$.

7. oh ok thanks

8. so that maks it y=1x

9. just checking something, to calculate the normal do I inverse it and make it negative in this case 1/-x but just so you know it isn't 1/-x it is just -x.

10. and how did you find x=0 and y=0, thanks

11. Originally Posted by Awsom Guy
and how did you find x=0 and y=0, thanks