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anonymous
 one year ago
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?
anonymous
 one year ago
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?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Why I am seeing this post as yellow colored? Or anybody else seeing the same?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0changed it a bit..had it wrong at first. I dont think finding an f[x] is very doable

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0its a paid question to the qualified helpers.. they go yellow

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6You 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
 one year ago
Best ResponseYou've already chosen the best response.0thnx, I can probably work this out from here..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0still not intuitive to me yet though.. even though I've done a dozen problems like this already

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6guess 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
 one year ago
Best ResponseYou've already chosen the best response.0ahh, I had got this far.. had it upside down dx/dy = 1.3 + Cos[n] / Sin[n/2]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6Looks good! simply flip both sides to get dy/dx you can play with derivatives just as fractions in single variable calculus

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ah gotcha, thank you lots, I couldn't see how to approach this problem at all

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ive worked out lots of single function derivatives, but this is my first 2 function derivative

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6You 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
 one year ago
Best ResponseYou've already chosen the best response.0I am not a qualified helper..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Have you tagged me somewhere writing this question?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank 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
 one year ago
Best ResponseYou've already chosen the best response.0waterineyes.. not tagged mate.. it shows yellow / orange color to all members..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The question in which you need a Qualified Helper, that question goes Yellow for all the users?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0@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
 one year ago
Best ResponseYou've already chosen the best response.0Do you see the advertisement under "ask a question". The blue owl is advertising "Get an Explanation. Ask a Qualified Helper."
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