This week in calculus we been reviewing from some old stuff we did in the earlier part of the year. We had a quiz and hopefully i did pretty well on it. We also have been doing something called an ALEKs. I think i'm going to like doing this stuff bc it made me realize i forgot hot to do some simple problems. I aslo went visit ULL this weekend and the engineer teacher told us how important it is that we remember this simple math. I'm looking forward to reteaching myself this stuff. Anyways bc we did old stuff in calc i will bring up some old formulas. You guessed it, the famous quotient and product rule formula. This week we mostly learned about how to apply the product rule and the quotient rule.
here is the formula for the product rule:
(recopy the first equation)(take the derivative of the second equation)+(recopy the second equation)(take the derivative of the first equation)
here is a example where you would have to
apply this rule:
(3x-2x^2)(5+4x)
since these two equations are being
multiplied you have to use the product
rule and plug in the formula
After doing so this is what you end up with
3x-2x^2)(4)+(5+4x)(3-4x)
then you simplify as much as
you can
12x-8x^2+15-20x+12x-16x^2
=-32x^2+4x+15
next is the quotient rule
here is the formula:
(bottom)(derivative of top)-[(top)(derivative of bottom)]/ (bottom)^2
the only way that this rule would not apply is if
you have a number instead of an equation
at the bottom of the fraction.
anyway here is an example using
the quotient rule:
5x^2-2/x^2+1
(x^2+1)(5)-[(5x-2)(2x)/(x^2+1)^2
from here, once again, you just
simplify as much as possible
5x^2+5-[10x^2-4x]/(x^2+1)^2
always keep the bottom of the problem
as is.
5x^2+5-10x^2+4/(x^2+1)^2
=-5x^2+4x+5/(x^2+1)
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