This week in Calculus was not that hard..we learned first and second implicit derivatives and then we learned some other stuff that I don't understand. I'm not even sure what its called, but I do not understand the stuff with drawing a shape then doing all the nonsense after..the new way of optimizing maybe?
But anyways, let me explain what I know how to do..
which is taking the second implicit derivative :)
You know when something is an implicit derivative when it has two variables, a x and y. Also, these types of problems have an equal sign. YOU MUST TAKE THE DERIVATIVE OF BOTH SIDES.
So, first you take the derivative of both sides like usual, but the new thing is, EVERY TIME you take the derivative of y, you must mark behind it dy/dx. This is for later reference that you took the derivative of y and not x.
Then you simplify it in terms of dy/dx.
After, if taking the second derivative, you take the derivative again and if you take a derivative of dy/dx, it becomes d^2y/dx^2.
Then you must simplify and plug in your dy/dx you got previously.
So, lets work an example problem!
xy = 4
(x)(dy/dx)+(y)(1) = 0 [TAKE DERIVATIVE OF BOTH SIDES]
x(dy/dx)=-y [START SIMPLIFYING FOR DY/DX]
dy/dx = -y/x [SOLVE FOR DY/DX]
Now, take the second derivative...
d^2y/dx^2 = [ (x)(-dy/dx) - (-y)(1) ] / x^2
Now plug in your dy/dx and simplify.
The thing I really don’t understand is the stuff we learned after this. When you are given a word problem and you have to just figure everything out..I’m having trouble figuring out what everything is and how you solve for whatever your looking for.
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When given a word problem it's best to try to underline key words and the values that go with them.
ReplyDeleteA rate will always be a dy/dt, dx/dt, or dtheta/dt or whatever the rate its describing. dr/dt is another one I just thought of.
I kind of just follow what Mrs. Smith makes us do...
Write your given...write your unknown...the basic equation and start working with that. It really does help whenever you write out what the problem already says in an easier way to understand than it being flooded by words.
okay so what i got from the related rates thing, is that you need to find your values first so ignore the rest except the important stuff, then you need to draw your picture then find the equation then solve.
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