Implicit Differentiation

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.