Implicit Differentiation, Calculus, TI 89, App, Program

Uploaded by Tommynnnnn on 06.09.2012

This video is on implicit differentiation, let’s get started, you press second alpha
to put the letters in my code here to get to my menu, and then you press alpha again
to get to the eight and the enclosed parenthesis. Then you press enter and up comes my menu
I’m already at the implicit differentiation one but you can scroll, ya know, up to what
ever you need here. If you are after this subject then that’s what you do. You press
enter to get into my program. I give you an example of it. You can use that here. You
have to press alpha first to put anything into that line on the Titanium, So were going
to do alpha y cubed plus y squared minus five times y minus x squared, press the equal sign
and minus four, you have to use the minus to the left of the enter button, not the one
the take away minus sign. And then you see what you’ve entered, check whether it’s
correct or not, if it is you press ok. And here’s the system, you differentiate both
sides with respect to x, the left side and the right side of the equation, which we did
here, and the answer is minus two x equals zero. You can see minus two x is the derivative
of minus two x squared. This is all partial differentiation, which you get in calculus
two mainly. And with respect to whatever, even though there are y’s, z’s or x’s
when you differentiate with respect to x, you just find the derivative of the x variables
in that function, and leave the others alone. That’s what we’ve done here. And then
you take the x here and move it to the right side of the equal sign, that’s algebra of
course. And then you are going to take the derivative of the left side with respect to
y, and this is the answer three y squared plus two y minus 5, which is the first derivative
of all these indications up here. And then the answer is dy dx . You take the right side
and divide it by the left side and here’s the answer. I give you the option to evaluate
it at a point. Sometimes a problem will ask you to do that. So we can do that now, you
have to press alpha and we can put in seven, and then maybe alpha minus six, and here’s
the x y point. Check if it’s right, if it’s wrong you can change it otherwise were going
to say it’s ok, and notice that the seven goes into the x’s and the minus six goes
into the y’s. You put that down on your paper, and here is the answer two over thirteen,
which is the slope of the line, rise over run. Notice that if you take two increments
up the y axis and over thirteen on the x axis and draw a line from that point down through
the center zero zero,. That’s the slope of that line. However it’s not a tangent
line. A tangent line is touching the point that you indicated, or asked to evaluate things
at, and I tell you that here just to remind you. And of course if you want to get that
you have to use the y equals m x plus b equation, which is in my programs also, I’ll show
you here. Go back to the main menu, number three. You press three and go back to the
main menu, and you can see that here is the equation of a tangent line, and that will
set that line right on that point. If you graphed it. Pretty neat huh,,
check out this program and other programs.