This week I learned that the 4 step process is really not the way to go. Here is an example of what not to do:
1. Find f(x+h)
2. Write f(x+h)-f(x) and simplify
3. Write f(x+h)-f(x)
h
4. Take lim f(x+h)-f(x)
h→0 h
Instead we learned a much easier method where you just apply the many rules of Derivatives to the equation and it gives you the answer much quicker than the 4 step process. For example take the equation 3x^2+5, first you take the exponent of the first part of the equation, which is 2, and you put it out front with the 3 and multiply them together, this will give you 6x^2. Then you have to take the exponent itself and subtract it by 1, so in this case you would get an exponent of 1 which means it would just read 6x. Last you would take the constant of the equation, which is 5, and turn it into zero. So the derivative for this example function would be just 6x. A lot easier than going through the 4 step process and taking up a whole page showing all of your simplifying and calculating. It is still important to know the 4 step process so you can use it as a fall back in case you can't seem to figure an equation out with the rules method.
1. Find f(x+h)
2. Write f(x+h)-f(x) and simplify
3. Write f(x+h)-f(x)
h
4. Take lim f(x+h)-f(x)
h→0 h
Instead we learned a much easier method where you just apply the many rules of Derivatives to the equation and it gives you the answer much quicker than the 4 step process. For example take the equation 3x^2+5, first you take the exponent of the first part of the equation, which is 2, and you put it out front with the 3 and multiply them together, this will give you 6x^2. Then you have to take the exponent itself and subtract it by 1, so in this case you would get an exponent of 1 which means it would just read 6x. Last you would take the constant of the equation, which is 5, and turn it into zero. So the derivative for this example function would be just 6x. A lot easier than going through the 4 step process and taking up a whole page showing all of your simplifying and calculating. It is still important to know the 4 step process so you can use it as a fall back in case you can't seem to figure an equation out with the rules method.
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