Isaac Physics 'Implicit Differentiation 2'

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domm1
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https://isaacphysics.org/questions/i...9-7215847615b0

I understood Implicit Differentiation for when you just had an equation in terms of, for instance, x and y, but this stuff I don't get.

Could someone explain to me how'd you approach RT when evaluating it for d/dV. Would it be T*dR/dV ?? I am confused.
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CaptainDuckie
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I don’t even do physics but I think I know this

Just simply expand and differentiate

T is a constant
Last edited by CaptainDuckie; 2 weeks ago
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domm1
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(Original post by CaptainDuckie)
I don’t even do physics but I think I know this

Just simply expand and differentiate

T is a constant so it’ll be just R on the right
This is an implicit differentiation question, read up on the concept and you'll see that it isn't just the normal kind of differentiation you'd do in Year 12.
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CaptainDuckie
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(Original post by domm1)
This is an implicit differentiation question, read up on the concept and you'll see that it isn't just the normal kind of differentiation you'd do in Year 12.
Yes, I’m not in year 12.

Implicit differentiate it, expand brackets, then use R as a constant on the right.
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domm1
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(Original post by CaptainDuckie)
Yes, I’m not in year 12.

Implicit differentiate it, expand brackets, then use R as a constant on the right.
But I thought that I'd be evaluating d/dV for each term, so for RT it would be 'd/dV*RT' which is that same as saying dRT/dV, but we're evaluating w.r.t V not R so what do I do? Apologies that my attempt to explain my confusion is all over the place.
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CaptainDuckie
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(Original post by domm1)
But I thought that I'd be evaluating d/dV for each term, so for RT it would be 'd/dV*RT' which is that same as saying dRT/dV, but we're evaluating w.r.t V not R so what do I do? Apologies that my attempt to explain my confusion is all over the place.
Are you doing part B?
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domm1
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(Original post by CaptainDuckie)
Are you doing part B?
Part A.
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CaptainDuckie
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(Original post by domm1)
Part A.
Write out what you think it is
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domm1
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(Original post by CaptainDuckie)
Write out what you think it is
I am quite clueless on this question so I'm really not sure, hence why I put this post out.
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domm1
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(Original post by domm1)
I am quite clueless on this question so I'm really not sure, hence why I put this post out.
It's not the entire expression which confuses me when differentiating, but certain terms, such as RT and -pb. How would you differentiate those terms w.r.t V? This is where my confusion lies.
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domm1
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(Original post by domm1)
It's not the entire expression which confuses me when differentiating, but certain terms, such as RT and -pb. How would you differentiate those terms w.r.t V? This is where my confusion lies.
When differentiating -pb w.r.t V you would use the product rule, such that d(-pb)/dV = -p*db/dV + b*d(-p)/dV , right?
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CaptainDuckie
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(Original post by domm1)
It's not the entire expression which confuses me when differentiating, but certain terms, such as RT and -pb. How would you differentiate those terms w.r.t V? This is where my confusion lies.
Taking a wild guess, use product rule
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CaptainDuckie
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(Original post by domm1)
When differentiating -pb w.r.t V you would use the product rule, such that d(-pb)/dV = -p*db/dV + b*d(-p)/dV , right?
I’d say that.

I think R would just be R
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DFranklin
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(Original post by domm1)
When differentiating -pb w.r.t V you would use the product rule, such that d(-pb)/dV = -p*db/dV + b*d(-p)/dV , right?
Yes, although it would be *way* less confusing to look at - d(pb)/dV
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domm1
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(Original post by DFranklin)
Yes, although it would be *way* less confusing to look at - d(pb)/dV
So if I were to evaluate each term I should get: (?)

d/dV*RT = T (from advice from CaptainDuckie)

d/dV*pV = p

d/dV*aV^-1 = -aV^-2

-d/dV*pb = -(p*db/dV + b*dp/dV)

-d/dV *abV^-2 = 2abV^-3 ?
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ghostwalker
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(Original post by domm1)
...
From what I recall of physics, R is just a constant, so if T is as well, then the entire right hand side is simply a constant.

Edit: It also gives a "correct" answer when you treat it as such.
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domm1
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(Original post by ghostwalker)
From what I recall of physics, R is just a constant, so if T is as well, then the entire right hand side is simply a constant.

Edit: It also gives a "correct" answer when you treat it as such.
I didn't think R was a constant?
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ghostwalker
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(Original post by domm1)
I didn't think R was a constant?
OK. Not sure what you're expecting in response.
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CaptainDuckie
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(Original post by domm1)
So if I were to evaluate each term I should get: (?)

d/dV*RT = T (from advice from CaptainDuckie)

d/dV*pV = p

d/dV*aV^-1 = -aV^-2

-d/dV*pb = -(p*db/dV + b*dp/dV)

-d/dV *abV^-2 = 2abV^-3 ?
Wait, re reading this, I think ghostwalker is saying that the right hand would be 0

Because its just like saying two constants multiplied by each other would differentiate to 0
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CaptainDuckie
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I think I got it
Last edited by CaptainDuckie; 2 weeks ago
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