Question

Given the functions
x[n] = 1.3n + Sin[n]
y[n] = 2(1 + Cos[n/2])
Assuming that these two functions are used to create a parametric plot where x = x[n] and y=y[n]

Ah.. but lets say that x[n] is..
x[Pi/2] = (1.3(Pi))/2 + 1 = 3.0420352248333655​

How would you combine these two functions to find the derivative of y= f[x]?

so you could work out the slope at that particular point?

Answer 1

Why I am seeing this post as yellow colored? Or anybody else seeing the same?

Answer 2

changed it a bit..had it wrong at first. I dont think finding an f[x] is very doable

Answer 3

its a paid question to the qualified helpers.. they go yellow

Answer 4

You may work the derivative directly w/o eliminating the parameter :
\[\large \dfrac{dy}{dx} = \dfrac{~\dfrac{dy}{dn}~}{~\dfrac{dx}{dn}~}\]

provided ofcourse \(\dfrac{dx}{dn}\ne 0\)

Answer 5

thnx, I can probably work this out from here..

Answer 6

still not intuitive to me yet though.. even though I've done a dozen problems like this already

Answer 7

guess it takes some practice, derivation is pretty straightforward though :

\[y = f((x)\]
plugin the parameterization and get
\[2(1+\cos(n/2)) = f\left(x\right)\]

differentiating with respect to \(n\) both sides gives
\[-\sin(n/2) = f'\left(x\right)*x' = f'(x)*(1.3+\cos(n))\]
\[\implies f'\left(x\right) = \dfrac{-\sin(n/2)}{1.3+\cos(n)}\]

which is same as what you would get using the earlier formula

Answer 8

ahh, I had got this far.. had it upside down
dx/dy = 1.3 + Cos[n] / -Sin[n/2]

Answer 9

Looks good! simply flip both sides to get dy/dx
you can play with derivatives just as fractions in single variable calculus

Answer 10

ah gotcha, thank you lots, I couldn't see how to approach this problem at all

Answer 11

Ive worked out lots of single function derivatives, but this is my first 2 function derivative

Answer 12

You will see more of these in polar coordinates... If you take calcIII, you get lot of practice while parameterizing for line integrals and surfaces etc. Just want you know that parametric equations are very common and important!

Answer 13

I am not a qualified helper..

Answer 14

Have you tagged me somewhere writing this question?

Answer 15

thank you, ganshie, I'll get this down..found a chapter on predator prey models, looks like it will clear it up for me, well and good..

Answer 16

waterineyes.. not tagged mate.. it shows yellow / orange color to all members..

Answer 17

The question in which you need a Qualified Helper, that question goes Yellow for all the users?

Answer 18

@waterineyes yes. OpenStudy has just added Qualified Helpers and OwlBucks which is their currency used to pay for immediate assistance.
You can buy OwlBucks with PayPal or any major credit cards starting at $1.99 for 10 OwlBucks

Answer 19

Do you see the advertisement under "ask a question". The blue owl is advertising "Get an Explanation. Ask a Qualified Helper."