In this question were given Bill you as a function of x y and zed and X Y and zed or each a function of teeth. So we're asked to express the beauty of the function of tea. The first we're gonna do that by using the trainable. So we have Do you buy d T I got you That is going to be equal to Di bi di t Uh um, and you can use question will personally, I like producto a little more So I am going to actually write that as X times that's apart. Negative one. Why times That's the power of negative one. So this means we're going to have to product cools here. I also let's do a part of school for the first term. That's going to be d x d t times that's apart. Negative one plus x times the by d t of that's a part of negative one. And then we will have the white 80 time sets of harm naked of one plus y times deep I d t. I'm said to the negative one. Okay, so now this is me x No team. Let's write that as sure as one over a sad and then we have waas x times. Um um directive of Zach Too hard, negative one by DT That's going to be negative. Said to the part of negative, too Times these are DT. And then this will be the why Day, tee times one over said this is gonna be why times the negatives that the negative too train will also be desired. So before we, um, continue with this, let's actually write down our the x d t d o y d t and d d t so that we can plug goes in So we have exes Coast Gertie. So that tells us the ex d t must be here Coast t and then train rolls all times Negative scientist, which is negative too. Scientist Coast. So why is equal to science? Great E So that means the wide 80 must be equal to two sighing t chain Wal Coast and he's at DT. Since that is one over tea. You can think of that as teeth apart. Negative one. So these I did. She must be negative. Er team to the negative too. I like to think of that as negative one over, he scraped. So now that we have these valleys, we can plug everything into this equation in terms of tea. S o d x t t. That's negative. Two sighing t coast E one over his head. That is one over tea. So one over one over t that just tea. That's Times Team. Plus, we have X. So that is co squared t times Negative said of hard Negative, too. Okay, so again, that is one over team. So what? The negative power means we flip it back up, so that's gonna be teeth grid, but with a negative sign for insights Naked of cheese grade. And these i d. T. Is negative one over. He's quick class. You I d. T s. That's two sighing t coast t times one over that. So that's just heat. And then Plus, we have our wine, which we know is sine squared t times negative sets of hard negative, too. That's negative t squared. And these i d t. That is negative one over TV script. So now that we have everything in terms of tea, let's cancel things up. So we have a negative T squared times a negative one over K squared, so that gets cancelled. Same thing here. We have a negative truth 90 CO C. Times t. And then we had the exact same thing, but a positive value. So they will cancel. So this names we are left with Coast Square T plus sighing square T So that means this is just equal toe one, because close, gritty plus size, great heat is an identity. So we're also actually asked to do to find you i d t. But instead of using Chang Ryul, we want to express the view in terms of tea first. So let's do it that way. So that tells us W is equal to X over set. So we're going to plug our X, and that's straight. And so we know X is equal to post where t So this is going to be co square t over one over tea, which is really tea time Coast, Grady. And that's plus y over said, which is going to be tee times signs 14 So this we can factor out the tea and it becomes coast grey tea plus science. Great e. So again we have our identity, which is equal to one. So we end up with W is just equal to teeth. So this means w the tea is just gonna be equal to one. So in this case, it was actually a lot easier to do with the second way might not necessarily always be the case. Um, but just for this particular went, this was easier. So now part B were asked to evaluate D W T T at a particular given Valley, and the given value is t equals three. But since D W T. T is a constant, it's equal to one. It really doesn't matter what value they ask us, because the W d. T. Of any value is going to be equal to one.