First Semester, Blog 4

11/12/2012

10 Comments

 
Chapter 3 is titled Derivatives.  Derivatives were first used in the 16th century.  What were they first used for?  Can you think of other uses?
10 Comments
Katie
11/12/2012 12:41:05 am

Derivatives have been used for a long time, which is very interesting. When we think of math we usually think of new theories and technology, but this shows us that mathematicians have been using complicated math for a hundreds of years.

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Katie Updated
11/12/2012 04:55:48 am

(The first time I posted the question part hadn't been put up yet, so don't judge me guys!)
I am not sure what a derivative is. I went to look it up, and Google told me it was "(typically of an artist or work of art) Imitative of the work of another person, and usually disapproved of for that reason."
This did not make much sense to me, because it did not seem to be involved in math at all. I looked up derivatives in Calculus. Google then told me it was "the derivative is a measure of how a function changes as its input changes." This sounded Greek to me, (probably because a good part of Calculus is, haha.)
I looked up more information, and it looks like some of the first derivatives were used by Greek mathematicians to make their equations much easier to understand.

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Rachael
11/12/2012 06:38:38 am

Derivatives were used by such scientists as Isaac Newton and Gottfried Wilhelm von Leibniz to measure how the change of the input of a function changes the function. I don't really know what that means, but it sort of sounds like when we talked about independent and dependent variables in 7th and 8th grade science. As the independent variable changes, so does the dependent. As the input changes, so does the function. Maybe these are two completely separate concepts, but I guess my brain connected them. I guess they could be used to make a guess as to what sort of effect a change will have, based on past changes. For instance, if Rachael asks 2 questions in math class, then she will understand a little better. Input: the 2 questions. Then the change would be reflected in Rachael's understanding. Therefore, this could be used to predict how much Rachael's understanding will increase in comparison with the number of questions asked. A couple questions=slight increase in understanding, while 2,548 questions=firm grasp on subject.

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michael
11/12/2012 11:08:20 pm

Derivatives was used for to measure a slope of the curve and the other way i can think of it being used is in physics to measure velocity which is V = D/T

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Jayce
11/14/2012 10:30:18 pm

The internet says derivatives are the measure of how a function changes as its input changes. I am not completely sure on what exactly that means, so I cannot give very good examples of how else they may be used. Although after further reading I will say that what Rachael said does say it best. The example of independent and dependent variables, because as the independent variable changes so will the dependent variable.

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Caitlin
11/14/2012 11:24:11 pm

Since I don’t know what derivatives are, I had to search for the meaning on Google. I found out that a derivative is the measure of how a function changes as its input changes. It is a controversial subject as to when derivatives were first used, but some say they date back as far as 1700 B.C. Looking at the way it was explained on the website that I found, I believe that derivatives were first used to make decisions, such as “If I choose this, my outcome will be this. But if I choose something else, then this will happen”. When thinking of other uses for derivatives, driving a car comes to mind. If velocity is increased, then the time it takes to get from point A to point B will be shorter. On the other hand, if the velocity is decreased, it will take a longer amount of time.

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Travis
11/19/2012 10:03:00 pm

Derivatives have been used for as long as mathematics have been used. Derivatives are classified as anything function, formula, or problem where the input will directly change the output. This classification applies to almost every function that is used in Calculus. If the value for X in a function is changed, then the value of the function and the Y will be directly changed.

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Tyler
11/20/2012 12:08:32 am

After a little research, I found what I think most people have found, that a derivative is the change in output from change in input. Looking for derivatives in the 16th century, I found that they took a big role in finance, as we see that this age is the introduction of sales to the world.

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Bailey
11/20/2012 12:20:59 am

Since I wasn't sure exactly what a derivative is, I had to turn to the internet. According to what I found, a derivative is a measure of how a function changes as its inputs change. In other words, a derivative is a measure of how one quantity changes in relation to another quantity. Sir Isaac Newton was one of the mathematicians to first use the calculus concept of derivatives in the 17th century. He used them in many of his calculations for his experiments, which often involved physics. Newton and other scientists used derivatives to find principles of motion, including acceleration and velocity. You could also use derivatives to find the slope and displacement of objects, and to determine more precisely how your variables would change in an experiment you were to perform.

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Megan
11/20/2012 11:03:16 pm

Derivatives are as old as the hills. They have been vital tools in the mathematic field as they have counseled hundred upon thousands of math wizards in their endeavours. It express how one quantity changes another.
You can use derivatives to find the prices of an individual item in a group of equally priced items. You can also discover distance, speed, or acceleration.

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