second drivitive of a parametric

I have a parametrically defined curve where i am trying to find the second derivative.

here is the problem:

and

I need to find the equation for the tangent line to the curve at the point defined by t = 1

finding

the dirivitive of x =

the dirivitive of y =

then, i evaluate t = 1 by plugging it into

Sorry having some formatting issues below i hope you can read it..

_______

after plugging in 1 for t

I get a slope of -1

so, then i need to take a second derivative

for the numerator its just 1

for the denominator its the derivative of x =

if so how do i evaluate that?

Re: second drivitive of a parametric

Quote:

Originally Posted by

**icelated** I have a parametrically defined curve where i am trying to find the second derivative.

here is the problem:

and

I need to find the equation for the tangent line to the curve at the point defined by t = 1

finding

the dirivitive of x =

the dirivitive of y =

then, i evaluate t = 1 by plugging it into

Sorry having some formatting issues below i hope you can read it..

_______

after plugging in 1 for t

I get a slope of -1

so, then i need to take a second derivative

for the numerator its just 1

for the denominator its the derivative of x =

if so how do i evaluate that?

You have a first derivative of

To find the second derivative you need to differentiate the first derivative which should be quite simple

Re: second drivitive of a parametric

Quote:

Originally Posted by

**e^(i*pi)**

To find the second derivative you need to differentiate the first derivative which should be quite simple

Thats what i thought - so there isnt a second derivative! or rather zero

So im left with just

for the second derivitive?

Re: second drivitive of a parametric

Quote:

Originally Posted by

**icelated** Thats what i thought - so there isnt a second derivative! or rather zero

So im left with just

for the second derivitive?

no ... you need to take the derivative w/ respect to x

Re: second drivitive of a parametric

Quote:

Originally Posted by

**icelated** Thats what i thought - so there isnt a second derivative! or rather zero So im left with just

for the second derivitive?

You have the wrong idea about the second derivative.

.

This may be simpler notation, is not strictly correct.

Let then

Re: second drivitive of a parametric

Hi plato - oh, lets see if i got this right..

so i take the derivative of y prime

over the derivative of x

Y`` =

because i dont need to take the 2nd derivative of denominator.

so i end up with the numerator as the same as the denominator?

Re: second drivitive of a parametric

Quote:

Originally Posted by

**icelated** Hi plato - oh, lets see if i got this right..

so i take the derivative of y prime

over the derivative of x

Y`` =

because i dont need to take the 2nd derivative of denominator.

so i end up with the numerator as the same as the denominator?

The first derivative is:

.

So

Re: second drivitive of a parametric

Well if

=

then, i take the second derivitive of that in respect to x but i cant do a

fraction over a fraction in latex.

taking the derivitive of in respect to x

I get

Which is exactly as the same as

So they cancel out for

= 0

Right?

Re: second drivitive of a parametric