Using 4U techniques in 3U (1 Viewer)

[Arrowshaft]

Hey there, was wondering if we are allowed to use 4U techniques such as implicit differentiation to both sides of an equation for related rates as its so much easier than using chain rule. If we cannot, is there an assortment of techniques we can use from 4U is there simply no techniques we can administer to achieve full marks on a question. Thanks.

 

[blyatman]

I would imagine it's fine, since there's nothing special about implicit differentiation: it's just the chain rule, and they only call "implicit differentiation" to make it sound fancy. Ask your teacher to be sure.

 

[Trebla]

The questions are usually designed so that you don’t need to use 4u techniques at all. Otherwise it disadvantages those who only do 3u.

 

[Arrowshaft]

The questions are usually designed so that you don’t need to use 4u techniques at all. Otherwise it disadvantages those who only do 3u.

Yes I agree but isn’t it more convenient to implicitly differentiate an identity without having to explicitly state the chain rule?

 

[Trebla]

Yes I agree but isn’t it more convenient to implicitly differentiate an identity without having to explicitly state the chain rule?

Implicit differentiation IS the chain rule. It's not exactly a new concept but rather just applying the chain rule in a different context.

If you asked a 3u student to differentiate , it's pretty much the same as differentiating implicitly where y=f(x). Both approaches explicitly use the chain rule.

Either way, it is extremely unlikely you will have a 3u HSC question where it is advantageous to use implicit differentiation compared to other approaches.

 

[Arrowshaft]

Implicit differentiation IS the chain rule. It's not exactly a new concept but rather just applying the chain rule in a different context.

If you asked a 3u student to differentiate , it's pretty much the same as differentiating implicitly where y=f(x). Both approaches explicitly use the chain rule.

Either way, it is extremely unlikely you will have a 3u HSC question where it is advantageous to use implicit differentiation compared to other approaches.

I understand but I’m saying in the context where the sample answers find an expression of say dV/dr and then dr/dt before stating the chain rule and proceeding to find dV/dt. My question is, can I just go straight to dV/dt without having to mention all this?

 

[Trebla]

I understand but I’m saying in the context where the sample answers find an expression of say dV/dr and then dr/dt before stating the chain rule and proceeding to find dV/dt. My question is, can I just go straight to dV/dt without having to mention all this?

So if you had
V = f(r)
By “implicitly differentiating” you get
dV/dt = f’(r)*dr/dt

The marker will read this as equivalent to using dV/dt = (dV/dr)*(dr/dt) anyway because you’re not really doing anything special outside the 3u syllabus. You are literally just using that very chain rule the solution uses when you “implicitly differentiate”.

Since it is identical there is no advantage using “implicit differentiation” in this context.

 

[Arrowshaft]

So if you had
V = f(r)
By “implicitly differentiating” you get
dV/dt = f’(r)*dr/dt

The marker will read this as equivalent to using
dV/dt = (dV/dr)*(dr/dt) anyway because you’re not really doing anything special outside the 3u syllabus. You are literally just using that very chain rule the solution uses when you “implicitly differentiate”.

Since it is identical there is like no advantage or saving using “implicit differentiation” anyway.

Ok thanks! Yeah, it was basically that “short cut” i wanted to use, sorry for the wrong phrasing.

 

[Trebla]

Ok thanks! Yeah, it was basically that “short cut” i wanted to use, sorry for the wrong phrasing.

It’s not really a “short cut” tbh.

The only difference is you either simplify the products separately then multiply or you multiply them first then simplify. If anything, the latter is more prone to error.

 

[Arrowshaft]

It’s not really a “short cut” tbh.

The only difference is you either simplify the products separately then multiply or you multiply them first then simplify. If anything, the latter is more prone to error.

Fair enough

 

[psmao]

Lol I barely studied for the motion parts, all I used is the mechanics knowledge from 4u.

if someone can teach me what d(1/2 v^{2}) even does, that would be much appreciated.

 

[greetings]

Lol I barely studied for the motion parts, all I used is the mechanics knowledge from 4u.

if someone can teach me what d(1/2 v^{2}) even does, that would be much appreciated.

Use it if they give an acceleration equation with respect to displacement (x)

 

[Arrowshaft]

Lol I barely studied for the motion parts, all I used is the mechanics knowledge from 4u.

if someone can teach me what d(1/2 v^{2}) even does, that would be much appreciated.

Do it if the acceleration is represented in terms of . But its basically the same thing as as we use in 4u for mech. You just integrate the LHS and RHS w.r.t. , but the just remains as the integral and the derivative ‘cancel out’ so to speak.