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differentiation

Posted on 2011-03-19
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Hi experts,
                        What is the application of differentiation. Where to use differentiation and what type of problems we can solve with this

Regards,
Vimal.
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by:abbright
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An example from physics is speed. If you have a function which describes the way you moved from a given starting point, the differentiation of this is the speed you move and the differentiation of this is the acceleration.
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by:vimalalex
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hi,
    Thankyou for your reply.pls explain some more detail.
Regards,
vimal
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abbright earned 250 total points
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Speed is the change of way over time. So if you have two points of time t0 and t1 you'll have two waypoints w0 and w1.
Now if you divide (w1-w0)/(t1-t0) you get the average speed between t0 and t1.
By moving t1 nearer to t0 you come closer and closer to the actual speed at time t0 (or t1).
By doing some limit calculus (don't know whether that's the right English word) you make t1 go to t0 and get the actual speed at time t0.
That's what differentiation actually does.
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by:TommySzalapski
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Any time something is changing at some varying rate (gas prices, temperature, speed, population) and you want to predict when it will reach certain values or do anything else with the information, you need derivatives. If the rate is always the same, then you just need algebra, but if the rate is changing in some quantifiable way, then you can't figure anything out without derivatives.
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by:vimalalex
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Hi TommySzalapski and abbright,

                            I am not able to understant properly. Pls explain with some other examples.

Regards,
Vimal.
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by:dhsindy
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More simply the first differentiation can be use to find the rate-of-change and the maximium and minimium points of functions.

A simple example, say: y=x^2 (y equals x squared) is our function.  The first derivation would be y'=2x.  If you set the derivative equal 0 and solve for x (x=0).  If you go back to the original equation and graph it you will find there is a minimum at x=0.
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by:InfoStranger
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Sounds like you want to study Statistics.  Not to simplify Statistics.  It is more complex than what I am about to explain.

Pretend you are at a bank waiting in line to see a teller.  There are multiple tellers.  We can use the Exponential Equation to analyze when you will see the next teller.  Calculating the waiting time it takes you to start in the queue to get to the teller.

Now, if you differentiate the Exponential Equation, you will get the Poisson Distribution.  This is like waiting at a corner of street at a stop sign.  You then count the number of car accidents that happens at that corner calculating the probability of a car accident.
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by:vimalalex
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Hi InfoStranger,
                      Can you explain the above decreption using the formulas in differentiation.

Regards,
Vimal
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by:vimalalex
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Hi InfoStranger,
                     Can you explain the above description using the formulas in differentiation.You have justed given as a note. Solve this using the differentiation step by step.

Regards,
Vimal
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by:TommySzalapski
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vimalalex, I think we are having trouble giving you what you want because we don't understand what you need.
Are you looking for us to work out some basic calculus proplems for differentiation like "Find the derivative of x^2-x+2" or are you looking for examples of practical applications for differentiation (which have been given)?
Can you please be specific in what you are looking for. What types of problems, etc? Give examples maybe. There are many different types of these problems with many different levels of difficulty.
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by:vimalalex
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Hi TommySzalapski,
                     
                         I mean, I am looking for the practical applications for differentiation which you have defined in sentence.

Regards,
Vimal.

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by:TommySzalapski
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Okay. Here are some great practical derivative problems with complete solutions. Please read the link
http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/maxmindirectory/MaxMin.html
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