find-the-derivatives-of-the-given-functions-v6-t2-sin-3-pi-t-3

Question

Find the derivatives of the given functions.
$$v=6 t^{2} \sin 3 \pi t$$

Tyler Moulton · Accepted Answer

Yeah, we want to find Dy Dx for the function Y equals six X squared sine three PX to do so we rely on the road in shortcuts we picked up throughout Singletary book up especially those related to trigger an electric derivatives. So the most relevant rules to solve this problem are now listed here have zero through three. These are rules zero DDX in Mexico&#x27;s coast, 60 D expose. Xnegative syntax and rules 123 The power roll products ruling chain were respectively, will rely primarily on real 01 and three to solve. We also have to use the product rule. So all four rules here will be used. Why equal six X squared sine three PX is already the most easily differential reform. So you can see through the derivative. This gives do I D X equals 12 X sign of three pi X plus six X squared plus in three PX three pi we use the product rule to separate into the some separated by this plus sign on the left. We have the power rule for six X squared on the right, the chain rule and rule zero for 73 PX. From this, we obtain our final solution for DY dx as 12 X. Sign three PX plus 18 Y X squared. Co sign three PX.

Robert Daugherty · Answer

section 3.6 number 26 were dealing derivative that involved the chain rule. So here were asked to find the derivative of s with respect to t. So we break it down piece by piece. What is the derivative of the sine function? That is gonna be the co sign. So the co sign of three pi t over to now, what is the derivative of three pi t over to best three pi over two. Plus what is the derivative of the co sign? That&#x27;s minus sign three pi t over to and then the derivative of three pi t over two is three pi over two. So this derivative is most like I can factor out three pi over two and then I&#x27;m just left with the co sign three pi t over two minus the sign of three pi t over to

Mike Gaerlan · Answer

in order to differentiate this to find our prime of tea here, we just need to take the individual component or the derivative of the individual components. So the derivative of two t squared or to T Q? That&#x27;s gonna be able to 60 squared by power rule. Same with this six square it of t. Remember, this is Tito the 1/2. So bring down the 1/2 and that becomes three times t to the negative 1/2 which is also the same as three over square root of tea. The man comma. And remember, this is three times t to the negative one. My power Will we bring down the negative one. And so we get this is gonna be good to negative three over and then T to the remember negative one minus one is negative two. So that&#x27;s gonna be square like that. So this is going to be our derivative here

Amy Jiang · Answer

Okay, So before we talk, start to take the government what you write this term in took in terms of negative experience. So we don&#x27;t have to use our question role. What? Taking to derivative. Okay. Gonna taking alternative. That&#x27;s G primal t vehicle to three times two of its six t squared For a start. It&#x27;s too nice one. So that&#x27;s this one. And plus six times seven. That&#x27;s negative. 42. Teacher of our of negative eight.

Kelly Hughes · Answer

First, I am going to rewrite my function so that there are no fractions. So I have GFT equals three t squared. And now again, I&#x27;m going to use negative exponents that way I don&#x27;t have any fractions here, so I&#x27;m writing this as six t to the negative Seventh power. Okay, from here, let&#x27;s go ahead and take the drive. So g prime of tea equals two times three is six t plus six times negative seven will give me a negative. So when he raced my plus sign and put negative 42 And then again I have to think to subtract one from my exponents. So negative seven minus eight is negative eight t Okay, Now I do not want to leave my answer with a negative exponents. So I&#x27;m going to rewrite this off to the side. So g prime of tea is equal to 60 minus 42 goes into my numerator and that negative exponents pushes my variable to the bottom and the export it becomes positive. So 16 minus 42 all over t to the eighth power. That is my final answer

Linh Vu · Answer

but functionally ask a coach, Julie times three about outscored the de and then makes it clear here. And we want a break it here to any case that two times good a function. And now want to find the s prime record that you have from the base A about other function on the tree, the river tive which should get equal to the A Power Uberti times and enough a times your Prem empty. So it is a formula here we can identify. This one will be the year 30 and the three here will be a therefore the S Bram the constant do Here we stayed the same. And now Thames three, Bella, skirt up D and Thames and and up three times discovered the derivative. And we know in the square root of TD riveted because you want number to skirt the tea. So no fall you should get now will be Teoh Alanna. Three attempts with the three Skurdal Treaty dividing by Ju square with the here to cancel over the Jew. So eventually the aspirin echoed you Ln of three times with the three skirt up, they divided by square with the day and that&#x27;s gonna be the aspirin were looking far

Problem

Find the derivatives of the given functions. $$y=…

Problem 16 Easy Difficulty

Find the derivatives of the given functions.
$$v=6 t^{2} \sin 3 \pi t$$

Answer

$\frac{d v}{d t}=18 \pi t^{2} \cos 3 \pi t+12 t \sin 3 \pi t$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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$\frac{d v}{d t}=18 \pi t^{2} \cos 3 \pi t+12 t \sin 3 \pi t$

Basic Technical Mathematics with Calculus

Anna Marie V.

Kristen K.

Samuel H.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Anna Marie V.

Kristen K.

Samuel H.

Michael J.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus