5

Use the properties of the derivative to find the following:r(t) 3ti + (t _ 1)j, u(t) = ti + t2j + Sck (a) r(t)(b) -[u(t) 2r(t)] dt(c) [(4t)r(t)] dt(d)~[r(t) u(t)](e...

Question

Use the properties of the derivative to find the following:r(t) 3ti + (t _ 1)j, u(t) = ti + t2j + Sck (a) r(t)(b) -[u(t) 2r(t)] dt(c) [(4t)r(t)] dt(d)~[r(t) u(t)](e)-[r(t) x u(t)]-[u(2t)]

Use the properties of the derivative to find the following: r(t) 3ti + (t _ 1)j, u(t) = ti + t2j + Sck (a) r(t) (b) -[u(t) 2r(t)] dt (c) [(4t)r(t)] dt (d) ~[r(t) u(t)] (e) -[r(t) x u(t)] -[u(2t)]



Answers

a. Use the Product Rule to find the derivative of the given function. Simplify your result. b. Find the derivative by expanding the product first. Verify that your answer agrees with part $(a)$ $$y=\left(t^{2}+7 t\right)(3 t-4)$$

Now we are given that F of X is defined as a X cubed plus B, X squared plus C. X plus D. In this problem. Uh And what we're asked to do is to find the derivative. Um And all we need to know is the power rule. And just kind of a reminder on the power rule is if you're asked to find the derivative of a constant, I'll use K. For constant. So and you're not thinking about that, see times X to the end power, It's equal to that constant times the exponent times x to the N -1 power. So that's all you need to know as well as I guess there's some formula that you just take the derivative of each term. So the constant times the exponents would be three a. And becomes X squared when you subtract one from this exponent plus to be X to the first power. But extra the first power is just one. Uh Plus the next term. Well, the derivative of a linear term is just the coefficient and then the derivative of a constant zero. And you don't have to write plus zero because it will not change the value of that problem. So this is your answer for the derivative using the power rule.

The problem is finally the derivative of the proactive function. R T is able to a plus B plus T square. See here, ABC electors. So we have a key problem. S e ko chiu zero plus e has after be passed to t Dr C. This is equal to Dr B Plus two t times, Dr C.

Of this over a want to use our cultural. Do you find the fallen vivid? So let's do that. So we have y popping that's equal to deserve it of of this term. So that's to t plus seven times are meaning, which is three t minus four and in plus conservative. This term, this is three times are remaining, Carrie. Okay, so let's expand this. So yet two times three, that's 60 minus a d plus 21 tea and then seven times for that's minus 28. And it will also have plus three t squared and then plus 21 t. Okay, so let's see. Um, we have a teeth word that's I have strong arrested beachy squared, and then or T, that's six it 2121. So we have six minus. It's plus 2121 heretical to 40 t and then we have, um, minus 28. Okay. And now, if reports, um, let me see if I could that correctly Shal that's six g. Sorry that you re a squared, so that's actually 90 squared. And instead of 40 we have negative change plus 2121 which is equal to 34. Okay, I know. Report Beat. It's expanders. So we have why that's equal to great. Cubed what is 42 squared? Plus 21 C squared and then plus negative. 20 or 28. So 21 minus four. That's 17. Okay. Mm. And now let's take charge of it. So we get nine t squared, plus two times 17. That's 30. 34 T minus 28. So we feel about two turns, which are derivatives, using a creditable on this, expanding their equal to the same thing.

For this problem. We're going to be finding first derivatives. So let's start by considering the derivative of FFT which is going to be T squared plus one cubed. So what we're gonna do is we're going to multiply the three in front giving us P squared plus one squared. And then using the chain road we're going to multiply this by treaty. So that would be our final answer. And then for the next one We're going to have the derivative with respect to pee. So that's going to give us six p. Using the power rule minus one half. Then for the next one it's going to be the derivative with respect to S So that's going to be one over to root S squared plus one. But by the chain role we need to multiply this by eight to S. So we do that. The truth cancel. And we're just left with he s on top that would be the first derivative there. Then we have first derivative with respect to T. So that's going to be a to a squared T plus B squared. Um That's it. And then we're going to find lastly the first derivative with respect to pee. So T squared even though it's a variable, it's just a constant when we're differentiating with respect to P. Such as going to give a zero plus um rather since we're taking the third power it's going to be three times T squared. Class, repeat. Not going to be squared now. And then we have to multiply this using the chain rule by the derivative. What's inside. So that's just going to be three, meaning that will happen nine right here, and that will be the final answer.


Similar Solved Questions

5 answers
L alongWhich Otthc Puth?IL 11 1{TnOnarn UUDDLLS1 1 ninor
L along Which Otthc Puth? IL 1 1 1 { TnOnarn UU DDLLS 1 1 ninor...
5 answers
Draw the major product expected for the following multistep reaction sequence: (2 points)MgBr 2) NHACl, Hzo3) HOCHzCHzOH, HCI (cat )
Draw the major product expected for the following multistep reaction sequence: (2 points) MgBr 2) NHACl, Hzo 3) HOCHzCHzOH, HCI (cat )...
5 answers
Vi thour i For mtercepts 9a) the find 1 unctioll 2 the I 1 1 1 pue graph #ppying (use algcbra 1 the 1 ]
Vi thour i For mtercepts 9a) the find 1 unctioll 2 the I 1 1 1 pue graph #ppying (use algcbra 1 the 1 ]...
5 answers
Enter your answer in the provided bor:Calculate the heat released when 64.0 g of steam at 129.0PC is converted t0 water at 44.0PC. Assume hat the specilic heat of #ater is 4.184 Jlg "C,the specilic heat of steam is [.99 Jlg "C,und AH,ap 40.79 kIlmol for water:
Enter your answer in the provided bor: Calculate the heat released when 64.0 g of steam at 129.0PC is converted t0 water at 44.0PC. Assume hat the specilic heat of #ater is 4.184 Jlg "C,the specilic heat of steam is [.99 Jlg "C,und AH,ap 40.79 kIlmol for water:...
5 answers
Aplace transfon oiy(t) is Y(e) Find the Laplace transfomd" (t) _ d"(t) 4v)+4v(), [erMs of Y(e) usira Y(0) = 3.H (0) = Y" (0) = 1 not forget to multiplication sign wher multiplying:)di"(t) 428(4) 4y() +4y()sin (&)
aplace transfon oiy(t) is Y(e) Find the Laplace transfom d" (t) _ d"(t) 4v)+4v(), [erMs of Y(e) usira Y(0) = 3.H (0) = Y" (0) = 1 not forget to multiplication sign wher multiplying:) di"(t) 428(4) 4y() +4y() sin (&)...
5 answers
5) Which of the followingaccurately represents an IMF interaction between water and the molecule below?6- OHOH_OHa)b)d) All ofthe aboveNone of the above
5) Which of the followingaccurately represents an IMF interaction between water and the molecule below? 6- OH OH_ OH a) b) d) All ofthe above None of the above...
5 answers
0 L 1 | 8 1 5836386 1F1 31 1
0 L 1 | 8 1 5836386 1 F 1 3 1 1...
5 answers
(6 pts) Find the exponential function and (2,16). Round k to 3 dec.Ce"s whose graph contains the points (0,8)
(6 pts) Find the exponential function and (2,16). Round k to 3 dec. Ce"s whose graph contains the points (0,8)...
5 answers
For the following problems, find the general solution to the differential equation.$y^{prime}=frac{y}{x}$
For the following problems, find the general solution to the differential equation.$y^{prime}=frac{y}{x}$...
5 answers
COCEOTcondeneee Foenm)ch,c(o] #(ch,) ,
COCEOT condeneee Foenm) ch,c(o] #(ch,) ,...
4 answers
Let k be am integer and by considering the derivative show that rk is increasing on [0,0). By dividing the interval [0, n] into n segments of width one and comparing the upper and lower sums show that:n -1 2 ik {7*s2 ikUsing this show that:knk <Eis Em+lyk i=1
Let k be am integer and by considering the derivative show that rk is increasing on [0,0). By dividing the interval [0, n] into n segments of width one and comparing the upper and lower sums show that: n -1 2 ik {7*s2 ik Using this show that: knk <Eis Em+lyk i=1...
5 answers
Calculate the wavelength and frequency of light emitted when an electron changes from $n=4$ to $n=3$ in the H atom. In what region of the spectrum is this radiation found?
Calculate the wavelength and frequency of light emitted when an electron changes from $n=4$ to $n=3$ in the H atom. In what region of the spectrum is this radiation found?...
1 answers
SciENCE AND MEDICINE The temperature dropped by $23^{\circ} \mathrm{F}$ from a high of $8^{\circ} \mathrm{F}$. What was the low temperature?
SciENCE AND MEDICINE The temperature dropped by $23^{\circ} \mathrm{F}$ from a high of $8^{\circ} \mathrm{F}$. What was the low temperature?...
5 answers
(10 points) Let f(r,U.:) =e-('+0*+8) (4 points) Calculate the gradicut VCOco fieldl Ff(6 points) Write dow equation for all Tectors ative Df(p) where( = Fucli that the directional deriv-
(10 points) Let f(r,U.:) =e-('+0*+8) (4 points) Calculate the gradicut VCOco fieldl Ff (6 points) Write dow equation for all Tectors ative Df(p) where ( = Fucli that the directional deriv-...
4 answers
4)- A double-pulley system as in the right figure above, has masses mi = 2.00 kg; mz = 1.20 kg, and m3 = 0.800 kg: (a) What are the accelerations of all the masses? (b) What are the tensions in all the ropes?
4)- A double-pulley system as in the right figure above, has masses mi = 2.00 kg; mz = 1.20 kg, and m3 = 0.800 kg: (a) What are the accelerations of all the masses? (b) What are the tensions in all the ropes?...
5 answers
Give one example of a physical process in the COVID 19 Iifecycle that could be used a5 a drug target to inhibit infection. Explain how that target would inhibit viral repication (Max 40 words)HIML Edrojca1 4 4 ` 4 - I = 3422 8 D 5 06 E 12pt Paragrph
Give one example of a physical process in the COVID 19 Iifecycle that could be used a5 a drug target to inhibit infection. Explain how that target would inhibit viral repication (Max 40 words) HIML Edrojca 1 4 4 ` 4 - I = 3422 8 D 5 0 6 E 12pt Paragrph...

-- 0.020551--