Post #18

In Calculus 18 weeks ago, I learned about derivatives, average speed, and instantaneous speed. For each of these math terms, there are different steps to follow. Many formulas are used and it is necessary to remember all of them. We learned around ten derivative formulas which include quotient rule, product rule, sum and difference rules, trig function rules, and rules for numbers with and without variables, and taking derivates of quadratics.I am very comfortable with taking derivatives by using the product rule.

The product rule is used when you are multiplying two terms such as this problem x² (x+4). First, you must know the formula, which is uv^1 + vu^1. In simpler terms, this formula means (copy the first term)(derivative of the second term) + (copy the second term)(derivative of the first term). Following along with the problem so far, you would have (x²)(1) + (x+4)(2x). You get x² because as the formula states, the first part of the problem is copying the first term. Next, you have to take the derivative of (x+4).

Knowing the derivative rule for variables without an exponent is equal to 1 and the derivative of any number is equal to 0, you obtain (1+0) for the derivative of (x+4). So far your problem should look like (x²)(1). The next step is to place the addition sign next in the equation. Then you should copy the second term (x+4), and take the derivative of the first. The derivative of x² is obtained by multiplying the exponent by the coefficient and then subtracting one from the exponent. (x²) = (2)(1) x²-1 = 2x.

Therefore your problem will then become (x²)(1) +(x+4)(2x). Simple algebra is used from then on, you should distribute the x² to the one and distribute the 2x to (x+4). Then add like terms to obtain your final answer of 3x² +8x.

One thing I am not comfortable with is finding instantaneous speed. Problems such as finding the instantaneous speed at t=2 where y=16t² confuses me. At first I though you just plug it in, but then I realized there was a special formula that confuses me. I know the formula, but I don’t understand how you decipher what is your “h” and what is the f(x). After the formula is plugged in and you do the algebra, what number are you supposed to plug in?

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