Isaac Physics &#x27;Implicit Differentiation 2&#x27;

I don’t even do physics but I think I know this

Just simply expand and differentiate

T is a constant

(edited 3 years ago)

Reply 2

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.

Reply 3

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.

Reply 4

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.

Reply 5

Original post by domm1

Are you doing part B?

Reply 6

Original post by CaptainDuckie

Are you doing part B?

Part A.

Reply 7

Original post by domm1

Part A.

Write out what you think it is

Reply 8

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.

Reply 9

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.

Reply 10

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?

Reply 11

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

Reply 12

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

Reply 13

DFranklin

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

Reply 14

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 ?

Reply 15

ghostwalker

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.

Reply 16

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?

Reply 17

ghostwalker

Original post by domm1

I didn't think R was a constant?

OK. Not sure what you're expecting in response.

Reply 18