DLS
  • DLS
Solve for dy/dx
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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DLS
  • DLS
\[\LARGE x=\frac{\sin^3t}{\sqrt{\cos2t}}\] \[\LARGE y=\frac{\cos^3t}{\sqrt{\cos2t}}\]
DLS
  • DLS
@hartnn
DLS
  • DLS
@amistre64 @terenzreignz @zepdrix

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terenzreignz
  • terenzreignz
Found it... it's on your original post :D
DLS
  • DLS
:O
terenzreignz
  • terenzreignz
But seriously... \[\Large \frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}\]
DLS
  • DLS
#inb4youtellMeToSolveItDirectly
DLS
  • DLS
that is gonna be a heptic calculation,can we do something to simplify things first?
DLS
  • DLS
you are never going to answer if you chose to solve it directly
DLS
  • DLS
\[\frac{dy}{dt}=\large (\sqrt{\cos2t} \times \sin^2t \times cost)-((\sin^3t) \times \frac{1}{\sqrt{\cos2t}} \times 2\sin2t)\]
DLS
  • DLS
we are gonna land no where how about something else?
terenzreignz
  • terenzreignz
That's somewhere all right, unless you wanted dy/dx in terms of x?
DLS
  • DLS
how about squaring and adding them?
terenzreignz
  • terenzreignz
somehow I think I'd rather subtract. \[\large y^2 - x^2 = \frac{\cos^6t-\sin^6t}{\cos(2t)}\]
terenzreignz
  • terenzreignz
adding leads to a dead end that I don't know how to factor...
DLS
  • DLS
alright :O
terenzreignz
  • terenzreignz
So, this is a difference of two cubes... \[\Large = \frac{[\cos^2(t) - \sin^2(t)][\cos^4(t)+2\sin^2(t)\cos^2(t)+\sin^4(t)]}{\cos(2t)}\]
terenzreignz
  • terenzreignz
Does this really help? The best I could hope for is to cancel out the denominator.. \[\Large = \cos^4(t)+2\sin^2(t)\cos^2(t) + \sin^4(t) \]
DLS
  • DLS
hmm..should be easy now
terenzreignz
  • terenzreignz
yeah, but that's y^2 - x^2
DLS
  • DLS
yeah i know
terenzreignz
  • terenzreignz
just tighten your belt and do it directly :D
DLS
  • DLS
lol
DLS
  • DLS
would you do this directly too? :O \[Prove ~That: \frac{d}{dx}(\frac{1}{4 \sqrt2}\log(\frac{x^2+\sqrt2x+1}{x^2-\sqrt2x+1}(+\frac{1}{2\sqrt2}\tan^{-1}(\frac{\sqrt2x}{1-x^2})\] =1/1+x^4
terenzreignz
  • terenzreignz
If all else fails, maybe :D
DLS
  • DLS
hmm \m/
DLS
  • DLS
very brave of you,master!
terenzreignz
  • terenzreignz
brave? No desperate? maybe...

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