9/26/2023 0 Comments Khan academy advanced calculusSo we're going to do the same thing, the derivative with respect to t, is going to be, and once again, we just use the power rule, four times four is 16t to the third power. To t of negative six, well that's just zero, so that's the rate ofĬhange of the x component, with respect to t. You're going to get negativeįive times t to the five, minus one power, so t to the fourth power. Power rule right over here, five times the negative So the x component, with respect to t, if you were to take the derivative, with respect to t, whatĪre you going to get? Well we're going to use the The respective components, with respect, take theĭerivative of the respective components with respect to t. Take the first derivative, h prime of t, was as you'll see, it's actually quite straight forward. So now that we have that out of the way, what we're interested in is, well let's find the firstĪnd second derivatives of h with respect to t. Sometimes you'll just hear people say, well, let h be a vector valued function, and they might not Vector valued functions with an arrow on top to make it explicit that this is a vector valued function. Representing the same thing, it just has a different notation. Plus two t, plus one, is multiplied by the vertical unit vector. So you might see something like that, where that's the unit Use what's often viewed as engineering notation here, where the x component is being multiplied by the horizontal unit vector. And you are probably familiar by now, that there is multiple notations for even a two dimensional vector. X component of the vector and the y component of the vector. T, it's a function of t, and so you give me a t, I'm not just going to give you a number, I'm going to give you a vector. Vector valued function h here, and when I say vector value, it means you give me a
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |