Derivatives

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Melody:

140403 garage door derivative.JPG

Let me define theta with this symbol &

I think what is the case here is that & is a fuction of x.

Then lets split y = xcot& + 1 - 2fcos&
into
y = y ₁ + y ₂ where y ₁ = xcot& and y ₂ = 1 - 2fcos&

then dy ₁/dx = cot& + x*d&/dx(cot&) = cot& + x* -csc ²& * d&/dx

Note that: -csc ²x = -(cscx) ² = -(1/(sinx)) ² = -1/(sin ²x), because cscx = 1/(sinx)

Therefore we have;

dy ₁/dx = cot & + x * -1/(sin ²x) * d&/dx

then for y ₂ we have

dy ₂/dx = 2fsin& * d&/dx

then dy/dx = 2fsin& * d&/dx + cot & + x * -1/(sin ²x) * d&/dx = cot & + (2fsin& - x/(sin ²x))d&/dx

Let me post this first before I look at the second part of your question

Melody:

140403 garage door derivative.JPG

I see ROM already answered in the meanwhile,

for the second part, it could also be that d&/dx = 0

Reinout

Rom and Reinout have answered the first part, so for the second part:

dydx2.PNG

Thank you all, much appreciated

I know a little more about derivatives and a little more about LaTex.
Putting this together was a real struggle.
I can't do chain rule unless I put in 100 extra steps.
This is my LONG version. (expanded from Rom's and reinout-g's - thank you)
Thanks Alan for the last bit. That was easy after all.

LaTex creates files as pdf's and I don't think I can bring pdfs into the forum. What is the best way around this?
I actually rotated this one, snipped it and then rotated it back again but it lost clarity. Also if the output was much longer it still would not have be adequate.

140404 Garage door derivative 2B.jpg

Melody:

Thank you all, much appreciated

I know a little more about derivatives and a little more about LaTex.
Putting this together was a real struggle.
I can't do chain rule unless I put in 100 extra steps.
This is my LONG version. (expanded from Rom's and reinout-g's - thank you)
Thanks Alan for the last bit. That was easy after all.

LaTex creates files as pdf's and I don't think I can bring pdfs into the forum. What is the best way around this?
I actually rotated this one, snipped it and then rotated it back again but it lost clarity. Also if the output was much longer it still would not have be adequate.

140404 Garage door derivative 2B.jpg

Nice!

What did you use for that LaTex part, everyone seem to be using it but me...

Hi Reinout,
I've been meaning write a post on LaTex for a while now.
I think there are a lot of different versions.
But this is where i learned most of it. The basics anyway.
I've only been using it for about 4-5 months. I hadn't heard of it before then.
https://www.youtube.com/watch?v=SoDv0qhyysQ&list=PL1D4EAB31D3EBC449
This is the first in a serious of clips done by Michelle Krummel. I think she has done a good job.

I dont think that Alan know LaTex. He uses MathType. (I think)
LaTex is the one that internet users use.
MathType is an add-on in 'ms word'. It is more used for documents.
When I was teaching we did all our type setting using MathType. (or just equation editor which was the free included version with ms office.)
I guess I swapped to LaTex because it is conveniently included in most forums.

Anyway that should get you started.

one sneaky trick you can use is to go over to the other forum and do your latex there, MHF has a very nice rendering engine now, and take a screen shot.

Crop it down and save it and upload it here.

Rom:

one sneaky trick you can use is to go over to the other forum and do your latex there, MHF has a very nice rendering engine now, and take a screen shot.

Crop it down and save it and upload it here.

thanks for the tip