Question
Let @ cOs T_ sin(1 )i - ertk_ Find V(V . @)
Let @ cOs T_ sin(1 )i - ertk_ Find V(V . @)
Answers
Find $\mathbf{r}^{\prime}(t)$. $$r(t)=\langle\arcsin t, \arccos t, 0\rangle$$
Okay here we are going to find our derivative of our vector valued function. Now looking at my three different components, I can see my first two are going to need to use product rules. So sometimes I like to let myself know what I'm doing before I start actually diving in. Okay, so our prime of T. Is going to equal now for that I component. We're going to do a keep derivative plus derivative keith and that's all in our eye direction. Now for our next piece we're going to have a keep derivative. The derivative co sign is a negative sign and then plus derivative keep. And then our last component, RK component, the derivative of tea, is just one.
Hello. We have a problem. # 79 In this village. Right 70. In terms of cost cost equal to in terms of course. No problem. And this is th zero too. Bye bye too. So this isn't the first quadrant So cost he has to be positive will be using the pythagorean identity. Science square T plus cause quite equal to one. So Science Square T. Will be equal to 1 -1 causes square T. Scientists will be equal to Plus -1- Causes Quality. But since he is in quadrant one, so we'll be just using positive. So one of minus causes quality. Scientific Well, thank you.
We're going to find the derivative of our vector valued function. Now look at our components. We're going to be looking at finding the derivative of each component separately. Are I. Component has a T. Co sign T. So we are going to have to use the product rule for that. So we're going to do a keep derivative, which is a derivative of cosine, is a negative sign T. And then plus derivative. Keep in the derivative of tea is just one. Now for RJ component, the derivative is just going to be a negative two and then it will become a co sign of T.
Okay, so here we have s is sign t over one minus co sign team. We want t S t t. So that's going to be This is a question to function. So the derivative is the bottom which is one minus curse Mt. Times the derivative of the top, which is co sign team minus the top Sai Inti times the derivative of the bottom which is zero minus the droop of CO santi, which is minus sign Inti minus to home. Careful. Mina Society, the derivative of one minus kasan. T is minus minus. Scientists actually plus seventy Great All over one minus co sign T Square. It's the dream.