Here is an example of a Implicit Differentiation test problem solved by the TI-89

Raw Transcript

Hello this is Tom for EveryStepCalculus.com again. I’m gonna do implicit differentiation, and this is a test problem that a person sent me and tried.  Didn’t do very well at. Would have done well with my program but I’m gonna show you how to do that.
or how it would have been solved if he had my programs um… index 8 to get to my
menu
and we press enter, were already on implicit differentiation
so I’m going to go there you can scroll that and
gonna add the
function, or equation
you have to press alpha before you enter anything in my entry lines in my
programs
Your going to press alpha, and put in
X cubed
plus 3
times X squared
times y
plus y cubed
equals 8
It’ll show you what you have entered
you can change it if you want, I say it’s okay
and your taking the differentiating both sides
d/dx of x cubed, d/dx of 3 times x squared times y, d/dx y cubed and 8
this is product rule because you have a times sign between there
I do each one for you
d/dx of x cubed is equal to 3x squared
you write all this on your paper d/dx of 3 x squared times y
I use the product rule…
and I show you that if you wanna the all
the formula for product rule, here’s the answer
6xy plus this
dy/dx of course and then
y cubed etc…
mark everything down on your paper and then the other side d/dx of 8 is equal to
0 this is the equation here
your separating dy/dx in certain sections
keeping the other ones without dy/dx in another section of the equation
and so here’s your answer
-3x squared minus 6xy you write all this on your paper
you get an A in this problem pretty neat huh? every step calculus dot com goto my site,
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