Need help on 'easy' questions

[vidang]

i seriously don't get these 'rate' questions at all
come up countless amount of times on exams
after I derive i don't know where to go from there?
something about using the chain rule? anyone care to explain

[TrueTears]

for Q 4.

dV/dt = 8

now we need to find dh/dt when x = 4

now dh/dt = dV/dt * dh/dV

we can dh/dV finding dV/dh first by deriving V(x) and then flipping it.

[brightsky]

Question 6

We want to find dr/dt.

We know that dr/dt = dr/dV dV/dt.

We also know that V = 2pi r^2, so dV/dr = 4pi r, dr/dV = 1/(4pi r). So at r = 30, this is 1/(120pi)

We are given the constant rate that is dV/dt = 10.

Hence dr/dt = 1/(120pi) * 10 = 1/(12 pi).


Generally, for these sorts of questions, you can follow a generic formula:

1. First state what you need to find (e.g. dr/dt from example above)
2. Then you need to use the chain rule. From example above, we know that the chain rule gives dr/dt = dr/d(something) * d(something)/dt. You can find the other 'something' using the info provided in the question. In this case, 'something' is V.
3. Find the product by using some algebra/calculus knowledge.
4. Substitute the point at which you want to measure the derivative. In this case, it is at r = 30mm.
5. Sub everything in and calculate.
6. State your final answer.

[schnappy]

Why do people make this so complicated.

You'll be given a rate. Write this rate in the form of dA/da.
You'll need to find a certain rate. Identify it and write it in the form of dB/db.
Say this (Write it down):
[The rate I need to find] = [Given rate] * [Another rate]

You need ot just look at the fraction to work out what needs to be the 'Another rate' so you find out what the rate you need to find is. In your first example, you're given dV/dt = 8, and asked to find dx/dt. You need to introduce dx, keep dt, but piss off dV.
dx/dx = dV/dt * dx/dV

Introduce dx/dV, you're told what V = in terms of x... find dV/dx, and flip the answer upside down. Sub into the above fraction multiplication and the rest should be simple.

[vidang]

^ great explanation thank you

[Stroodle]

Here's another really simple explanation on how to approach these questions. Basically the same as what everyone's telling you, but maybe the examples will help..

[cypriottiger]

i look for key terms in the question to help me identify what each bit of info means, so say a depth of sphere cup is increasing at 4 cm s, then you know the units are depth, h, and time, s, so 4=dh/dt. it may ask, find the rate at which the volume in increasing.
so rate implies time, and then volume, so the question is asking for dV/dt. using the chain rule from your formula sheet, have dV/dt be your first fraction, and then use the formula to fill in the blanks for what u need to find. do this write and odds are it will earn you a mark
therefore dV/dt= dV/dr x dr/dt
now if dV is on top, then you find the derivative of the shape in this case a sphere so V= 4/3(TTr^3) -> dV/dr = 3x4/3=4TTr^2 (TT is pie btw)
the question will also say, find the rate when r=2cm
so dV/dr is flipped because its like saying dy/dx instead of dx/dy, so dV/dr becomes 1/(4TTr^2) at r=3 -> 1/(36TT)
no just fill in the gaps
dV/dt=1/(36TT) x 4 (from the beginning)
= 4/36TT ---> 1/9TT
tada! literally no memorising needed, as long as your derivativation skills are ok any question is possible with no experience needed. try a few practise questions before the next prac exam to get the hang of it so u dont spend 15+mins on a 3 mark qn

[Studyinghard]

i wish the whole exam are these types of questions (Y)

[TyErd]

i wish the whole exam are these types of questions (Y)

+1