Video for finding dy/dx with the Quotient Rule
Video for finding dy/dx with the Quotient Rule:
Raw Transcript
Hello everyone Tom from EveryStepCalculus.com. I’m going to do a problem that a student asked to be solved. See if my programs could do it. So here it is. index 8 to get to my menu and we scroll to in the menu scroll to log problems and we want to differentiate so we’re going to choose number seven you can scroll or with the cursor, or else choose a number, I like to choose the number before it quicker and number two we want to do a log of base…something. We’re going to enter our function. You have to Press Alpha before you enter anything into these entry lines here, your going to press alpha and then we have to gonna press actually second alpha so we can put in the log which is l o g and then um. alpha to put the 5, for the base and then parentheses. And we’re going to put the square root of x divided by always use parentheses in the denominator 5 minus x, close off the parentheses. I always show you what you’ve entered so you can change in case you made a mistake, say it’s OK. And we have y equals log of this the calculator changes this because it switches around the 5-x to x-5 there’s a log rule applying here dy/dx equals log of a(u) this is the base a and whatever’s in here is the u and here is the formula for the log rule. You write that all in your paper and u is this part of the problem and so we’re going to do dy/dx that’s what it’s asked to find and we’re putting this into the log rule. Now this part here, derivative of this section here’s a quotient rule that equals this right here mark that down in your paper and here’s the answer log of 5 e times this part here. Pretty neat huh? EveryStepCalculus.com. Go to my site, buy my programs and pass calculus and subscribe to my channel if you want to hear and see more videos.
Quotient Rule Step by Step
Raw Transcript
So this is a video on the quotient rule as it applies to my fabulous programs
that I’ve programmed on the Titanium or any calulator that uses the ti system and that can do an integral or derivative where my programs can work uhm, there’s so many now that they’re almost overloading the calculator but uhm I’m going to show you this quotient rule works I’m going to turn it on here and get out of this program here and get to the home screen F one eight clears the screen and then we can clear the home entry line by the clear button here you have to put index eight closed parenthesis on here, we do that by going second, here’s second alpha, it makes this dark, therefore you have the letters you can put in letters i n d e x and then alpha again to put in the numbers- number 8 and the closed parenthesis and we’re into my program you’ll notice that this is, you can scroll up with the scroll keys to go up as far as you want, there’s all kinds of things in here product rule quotient rule, difference quotient, limits, trig integrals and derivatives, not everything in a calculus book is in here, but just what I’ve done on tests, and I wanted to pass test, that’s what I did using the calculator uhm, so I’m going to go down to all alphabetical, so, here’s the product rule I showed you in another video, quadratic formula here’s the quotient rule right there, we’re gonna wait for it to load here, ah there it is the quotient rule and you are taking one function and dividing it by another function.and the formula is: g of x times f prime of x minus f of x time g prime of x all divided by g of x squared, that would be fun to do on a test wouldn’t it, from memory, I don’t think so, but maybe anyways much easier with this let’s put something in here we have to put the parenthesis first then put a divide sign in between it as I show you up here, we have to press alpha, and there’s the, we have to put in x squared plus three x divided by uhm let’s say two times x plus five and we have to press it twice, let’s see if we’ve done that, x squared plus three times x over two x plus five, very good and you always have a chance to change my programs or change what you’ve entered in case you’ve made a mistake, that’s always — and so here we go we got the g of x plus f prime of x and g prime of x times f of x, over g of x squared and we work it down here, we work and keep doing the calculations, which you write on your paper, don’t even think about it just write it. write down the next thing, write sloppy. nerds and mathematicians love a to write sloppy and all over the page, you do the same unless you already do that, that’s fine and we have, ahh the answer is two x squared plus ten x + fifteen, all over two x + five squared all step by step, working it step by step ah pretty neat huh? check it out at my web site every step calculus dot com