Explaining differentiation on sample exercises

Help please

Doesn't Differentiation mean "to take something from another thing"?
How is this related to Limits?


I know F'(x) = Lim {f(x) - f(a)} \ {x - a} As x goes to a

But, What is this rule to do with "taking something from another thing", like differentiating the speed from distance=f(time) or acceleration from speed=f(time)

________________________________________________________________

Why when talking about a problem related to rates of change we just use differentiation, for example, A balloon being filled with air ... blah blah blah , The equation that relates V(the volume) to r(the radius) is V= ¾ ψ r , ψ is pi

In other words what is that(the balloon problem) to do with limits ?

Added after 1 hours 56 minutes:

hello?

Added after 1 hours 7 minutes:

please, I have an exam after 36 hours :S

Added after 1 hours 12 minutes:

**broken link removed**

Re: Help please

hope am not posting this late..

you know that the rate of change of a certain quantity (f) in respect to another quantity (x) (where f is a function in x) is:
{f(x2) - f(x1)} \ {x2 - x1}

this is the rate of change of f when x changes from x1 to x2.
now if we want the rate of change for f at a certain x, we can simply take the limit of the rate of change as x2 goes to x1, as if we are making them a single point!

in your formula (a) is x2-x1, and by taking the limit as a goes to 0, you are finding the rate od change at a certain point x. and this is the definition of the derivative.

you find differentiation in problems that ask for rate of change because it is asking for the rate of change at a certain point! in your question he asked how fast (the rate of change of the height in respect to time) when the water is 4 inches deep!

we differentiate distance to obtain the instantaneous speed at a ceratin time, cause by definition speed is the rate of change of the distance in respect to time, and it is instantaneous because it is at a certain time.

in your question you are given that the volume of the water is changing with respect to time by a rate 2/3 and you are asked for the rate of change of the height at a certain point, and you know the volume as a function in the height, so you simply differentiate both V and H in respect to time and substitute with the values.

you should understand what is the question asking for, and in respect to what you must derive.

good luck in your exam

Help please

they burnt my school LOOOOLL
so ur not late

thanks for your demonstration , that was really helpful

Re: Help please

differentiating means taking or deriving from sumthing.if u r having a unit step function and ur differentiating it then the result will b an impulse delta function
d/dt[u(t)]=delta(t)

Re: Help please

Hi,
While on this subject of differentiation, another point of view of the subject is that it gives the slope (tanΘ) of the function at the point.
Regards,
Laktronics

Help please

thx, for help

Added after 48 seconds:

you are king ,good luck