This week in calculus we had our exam. B-Rob gave us until Wednesday and Thursday to take our exam so we could have some extra time to do our packets and study. We did a lot of reviewing this past week to prepare us for the exam. We reviewed things like limits, derivatives, the first derivative test, the second derivative test, Rolle's theorem, mean value theorem, and ways to find either the origional function, first derivative, or second derivative from looking at a graph. Friday, after we were finished with our exams, we learned new material. This new material was implicit derivatives. They're just like regular derivatives, except there is more than one variable in the function.
The steps for finding implicit derivatives are as follows:
1. Take the derivative like normal of both sides
2. Every time you take the derivative of y, note it wigh dy/dx or y'
3. Bring all the dy/dx terms to one side and the regular ones to the other side of the equation
4. Solve for dy/dx
Also for implicit derivatives, if a problem is asking for the slope and it only gives you an x value, you plug the x value into the origional function to get a y.
Another thing to remember for implicit derivatives is if you see a problem that has x values on one side of the equal sign and y values on the other, leave them as they are and take the derivative and deal with them later.
Ok, this week my question is on implicit derivatives. I know the steps and I can follow them, but when I'm taking my derivative, I always forget to note dy/dx after I take the derivative of y or I get confused on where my dy/dx goes. If anyone knows a way to help me organize my work and a way to remember where to put dy/dx, please let me know.
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dy/dx goes everytime after you take the derivative of y.
ReplyDeletesay you have xy= 9
doing the product rule, you copy x the TAKE THE DERIVATIVE OF Y so you have to note it with dy/dx the rest of the derivative does not need to be noted because you copy y and take the derivative of x, not y.
your work would look like:
x(dy/dx)+ (y) (1)= 0
so dy/dx = -y/x
As of remembering to note it, I guess it just comes with practice.
you take the first derivative then substitute dy/dx for your y-value then you just solve for dy/dx.
ReplyDeleteImplicit derivatives are easy you just have to remember to note dy/dx after taking the derivative of the y. Take it like normal and everytime you mess with the y write dy/dx in back of it. It's just the process of remembering it then you'll do fine. Solving for it is easy just get it by itself :)
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