anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Why I am seeing this post as yellow colored? Or anybody else seeing the same?
anonymous
  • anonymous
changed it a bit..had it wrong at first. I dont think finding an f[x] is very doable
anonymous
  • anonymous
its a paid question to the qualified helpers.. they go yellow

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ganeshie8
  • ganeshie8
You may work the derivative directly w/o eliminating the parameter : \[\large \dfrac{dy}{dx} = \dfrac{~\dfrac{dy}{dn}~}{~\dfrac{dx}{dn}~}\] provided ofcourse \(\dfrac{dx}{dn}\ne 0\)
anonymous
  • anonymous
thnx, I can probably work this out from here..
anonymous
  • anonymous
still not intuitive to me yet though.. even though I've done a dozen problems like this already
ganeshie8
  • ganeshie8
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
anonymous
  • anonymous
ahh, I had got this far.. had it upside down dx/dy = 1.3 + Cos[n] / -Sin[n/2]
ganeshie8
  • ganeshie8
Looks good! simply flip both sides to get dy/dx you can play with derivatives just as fractions in single variable calculus
anonymous
  • anonymous
ah gotcha, thank you lots, I couldn't see how to approach this problem at all
anonymous
  • anonymous
Ive worked out lots of single function derivatives, but this is my first 2 function derivative
ganeshie8
  • ganeshie8
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!
anonymous
  • anonymous
I am not a qualified helper..
anonymous
  • anonymous
Have you tagged me somewhere writing this question?
anonymous
  • anonymous
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..
anonymous
  • anonymous
waterineyes.. not tagged mate.. it shows yellow / orange color to all members..
anonymous
  • anonymous
The question in which you need a Qualified Helper, that question goes Yellow for all the users?
UsukiDoll
  • UsukiDoll
@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
UsukiDoll
  • UsukiDoll
Do you see the advertisement under "ask a question". The blue owl is advertising "Get an Explanation. Ask a Qualified Helper."

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