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Find the derivative of the vector functionr(t) 3 In(19 _ +2)i+ V12+tj - 4e ~t kr (t) =...

Question

Find the derivative of the vector functionr(t) 3 In(19 _ +2)i+ V12+tj - 4e ~t kr (t) =

Find the derivative of the vector function r(t) 3 In(19 _ +2)i+ V12+tj - 4e ~t k r (t) =



Answers

Find the derivative of the vector function.
$$
\mathbf{r}(t)=e^{t^{\prime}} \mathbf{i}-\mathbf{j}+\ln (1+3 t) \mathbf{k}
$$

The problem is fine at the dinner Metis of provocative function that he is able to eat negativity he minus Tease Cube and have nt. So if art he is, they want you angsty. Why he through We Have Are You from? It's a cultural angsty prom. Why keep prom? I think he probably over half I should prom. But this problem this Lizzie you called, too. Eat connective T time. Snake to one one month's, three square on one over.

Okay. Find the derivative of this vector function. Uh This is a product here. So it's the first times the derivative of the second plus the second times the derivative of the first. All of that times I plus this is B times sine cubed T. So three be signed square T. Times the coastline of T E. T. And then plus three C. Co sign square tee times minus sign. Oh there was a J. There. Okay. Something cube. So three something squared times the derivative of the something three Because okay, So I end up with -80 mhm. I see -380 signed three T Plus A Coastline three T. I plus three B. Sine squared T. Cosign T. I don't know what that deep T. Is doing there, jay -3 C. Co Sign Square T. Sign T. Okay. Right.

To answer this question will use Terran three point over differentiation off vector valve function which states that if a function I de equal to hey, I this Jeez, let's thanks. Who king then I dash d is equal to if Dashti unless t dash thing. Hey, this key. So therefore, in this particular question, why and do you could be B q g do could be three d square And do you being you too by six. So now we need to differentiate each of them and combined them together to find the differentiation off function. I think so, Yeah. Cash the differentiation off the cube. So it iss three square g d is the differentiation off three t square. So that ISS 60 riches he used to they do six e and Etch Dash D is the differentiation off. Thank you by six. So that ISS two it's clear by six it is equal to the square by two. Now we combined them together. So my final answer, our Dashti is because to attach T which is three d square. Hi Bliss G Dash D, which is six less h dash d which is the square bye. Do So this is our final solution

Dear Eliot. Function is R P is equal to t to the fourth square root of T plus one and three over T Square. And while they want us to find the derivative, so we'll take the interpretive of each component and I'll get for tea with viral one t. I want half. Oh, over. Let's one over. Scary of ta bless Mint bar Gilligan on and see negative six over TV. Also the fire was it?


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