Implicit Differentiation Test Question

February 1, 2014 by Tommy Leave a Comment

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,
buy my programs pass calculus also
subscribe to me so that you can see other
movies and blog

Implicit Differentiation Video on the TI89 Calculator

August 29, 2013 by Tommy Leave a Comment

Raw Transcript

This is a video from everystepcalculus.com demonstrating how my programs work and I TI 89 titanium calculator and other calculators and a TI system for calculus and physics problems okay implicit differentiation my programs work on that and let’s get started yep for a second offer to put the letters i ndex in here and you have for itself but it but the a you can close parentheses press Enter into my menu I’m already at implicit differentiation you can screw whatever you want here press Enter and we’re gonna enter function you have to Press alpha before you enter anything in these and felines here’s member that alpha and let’s go 5 time X by minus 3 X squared why bus for six. I always show you what you’ve entered you can change it if you want notice that this is people’s six let it take to get a problem where there’s the this for a while the on this side will be here well you need to transpose it over to the other side so this would be a minus 4 y-o-u 6 -4 why so make sure you just have a zero or the constant right side 280 trickier s. I say it’s okay to press one here and you gonna take DD except every term and that function which I’m doing here show you write this on your paper right here ever gonna take the first term and you notice that is going to be the product because you’re multiplying functions times why X years so now I show you the steps for the product rule but you can go quickly if you practice and greatly answer which is this answer here and it separates the way TX terms into ones spot for the ordinary terms and the next term is another product rules so show you write that down to be interested here’s the answer and the you idea except for it four times why equals this you a geek and you a txt 660 said make it zero on the right side and of course the period accustomed 0 so we’ve grouped all the ordinary terms and that the way the xterm and equals zero you gonna transpose this now over to the right side because here change the signs the course does that automatically years the answer the way DX equals this and this let’s do it at a let’s evaluate a point as always fun. Press alpha to pointed to alpha now I value it at this point here again I show you you made a mistake and you’re gonna like these numbers and this is for the X’s in the y values rate here all entered in the year as the calculation 63 over to in a corset handed -1 30 arcane 31-point by is here’s the actual degrees ovett with you meet the this is rise over run maybe go up 63 points on the Y axes and over to the right and the xx’s draw a line from there down through the origin and that graph you you found the slope that my SAT point2 agrees. Pretty neat. everystepcalculus.com. Go to my site by my programs and pass calculus.

Implicit Differentiation

December 9, 2012 by Tommy Leave a Comment

Raw Transcript

This is a ti 89 Titanium program app. uh… regarding Implicit Differentiation. Let’s get started here

to enter my menu in my programs you have to press second alpha and then put the letters

i n d e x and then press alpha again enter the eight and the open and closed parentheses press enter and you’re into my menu many things on here, eliminating the parameter, e to the x integrals

anything you want for passing calculus and and uh… your homework we want, implicit differentiation and we’re going to enter our function. Press alpha, you have to press alpha before you enter anything in my menus or my entry lines alpha x cubed plus x squared times y cubed

minus three times y squared equals one. I show you what you’ve entered you can check your

entry here and see if it’s ok. I say it’s okay. And you notice within implicit differentiation your your taking the derivative of every term in that function on both sides and so we start take the first term take the derivative we take the second term but here’s a times sign between it, so we need to do the product rule on it and i show you how to do that here’s the formula, you write all this down on your paper f of x equals x squared, f prime of x equals two x g of x equals y cubed, g prime of x equals three y squared dy dx and here’s your answer if your professor doesn’t do that product rule and just comes up with this, then just put the answer down and then we continue with our derivatives of each term in that function and there’s the next one here’s the one on the equal sign, ya know, for the one and so differentiating both sides of the function. We get you write all this down

and here’s your answer now you can evaluate it at a point for instance you have to press alpha again. Let’s say press alpha four and alpha two show you again in case you made a mistake and then you write this notice you’re entering all the variables into your function and it shows you the slope of the line actually shows you also the the way the vector is pointing which is three hundred twenty eight degrees. Pretty neat huh? everystepcalculus.com. Check out my site, you’ll love my programs and pass calculus.

Implicit Differentiation

September 23, 2012 by Tommy Leave a Comment

Raw Transcript

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, everystepcalculus.com,

check out this program and other programs.