Question

I just don't seem to be able to understand how to get the second derivative of a parametric equation. Can someone walk me through it?

Answer 1

Okay, my parametric equation is x=3+3t^2, y+3t^2+t^3.
to find dy/dx you divide (dy/dt)/(dx/dt). Which I can do no problem.

Answer 2

For the first derivative I got for 1-((3t^2)/(4t)). Which the online homework problem says is correct.

Answer 3

To find the second derivative I have to find d/dt (dy/dx). I separated the two parts and got 0 for the one, of course, and then used the quotient rule on the -3t^2/4t part. Is this correct?

Answer 4

a paramentric eqution is also a vector equation:

r(t) = <x(t),y(t)> right?

Answer 5

Yes

Answer 6

x=3+3t^2 , y=3t^2+t^3
x'=6t , y=6t+3t

r'(t) = < 6t , 6t+3t^2 >

which is what youve got for the tangent

Answer 7

Lol, I mixed two problems in what I explained, but yes, go on

Answer 8

r''(t) is just the next derivative.

r''(t) = <6, 6+6t> if im reading it right

Answer 9

http://tutorial.math.lamar.edu/Classes/CalcII/ParaTangent.aspx

might help

Answer 10

bout 3/4 of the way down it goes into 2nd derivative

Answer 11

Right, but the question is asking for it in a certain form. Here is the question:

Answer 12

a tiff? really?

Answer 13

you got that in a jpeg?

Answer 14

Lol, here it is in jpg

Answer 15

I just sliced a portion of the window to get the picture

Answer 16

\[\frac{d^2y}{dx^2}=\frac{d}{dx}(\frac{dy}{dx})=\frac{\frac{d}{dt}(\frac{dy}{dx})}{\frac{dx}{dt}}\]

Answer 17

soo

dy/dx = 1+ t/2 stick this in the derivative thing for: 1/2

right?

Answer 18

\[\frac{d}{dt}(\frac{dy}{dx})\to \frac{d}{dt}(1+t/2)\]

Answer 19

Yeah, you're right. But what I have is a dy/dx = 1-3t^2/4t

Answer 20

or the right dy/dx .. lol

Answer 21

Sorry, I starting typing the first, which is pretty easy when I was actually going for a second problem. But this is the spot I always get confused. With that dy/dx I would lose the one and use quotient rule to solve for -3t^2/4t, wouldn't I? But when I do that it says I got the problem wrong

Answer 22

reduce it by t and you got -3t/4 which is simpler to derive

Answer 23

not reduce ..... simplify

Answer 24

Oh my Gosh!! I can't believe I wasn't seeing that! Thank you!

Answer 25

youre welcome