find-the-derivatives-of-the-given-functions-vleft4-csc-2-3-rright3-3

Question

Find the derivatives of the given functions.
$$V=\left(4-\csc ^{2} 3 r\right)^{3}$$

Tyler Moulton · Accepted Answer

we want to find the derivative. Dy dx for the function. Why equals four minus coast. You can&#x27;t square of three are cubes. So to solve, we&#x27;re going to proceed to define the relevant shortcuts that we need to solve its derivative specifically, we&#x27;re going to rely on trigonometry derivatives we&#x27;ve recently learned. So the relative derivatives are listed here. Of the six trigger derivatives that I&#x27;ve listed. We really only need to rely on DDX coast. You can&#x27;t X equals negative post. You can&#x27;t tangent X. We also are going to use the chain rule to solve so we have Y equals four minus cost. You can&#x27;t square through. Our cube is already in its most easy different to perform, which means we can proceed to the derivative. Thus we have dy Dx equals by the chain rule three times four minus coast. You can&#x27;t square three R squared times what&#x27;s inside which is negative. Two coast, you can&#x27;t three are times negative coast. You can&#x27;t three Arco tangent three times three. Which your final solution DY DX equals 18 times four minus coast. You can&#x27;t square through r squared times cause you can&#x27;t square three arc tangent three are.

Amrita Bhasin · Answer

we know we&#x27;re gonna have to apply the chain role for this. So taking the derivative we bring the explain it down becomes the new coefficient, make the export, and one less so instead of three now becomes too. And then we multiply by the driven of a four mice X squared, which, as you know, is negative two acts. The derivative of Forrester, Cyrix. It&#x27;s a constant simplifying to f prime of axe equals negative sex acts times four minus X squared, squared.

Robert Daugherty · Answer

section 3.6. Number 33 were dealing with first derivatives and involving the chain rule. So as with many things and calculus, you have one rule. But other rules apply, so this will involve you. Look at this problem not only the chain rule, but the product rule is well, so why prime going to be equal to Let&#x27;s take the rivet of the first term. So that&#x27;s four times four x plus three cubed times the derivative what&#x27;s inside the parentheses, which is just four. So that&#x27;s the derivative the first term. So times the second term. And then, if I&#x27;m continue at the product rule, it&#x27;s gonna be plus that first term times the derivative of the second term, which is minus three X plus one to the minus, four times the derivative of what&#x27;s inside those parentheses, which is simply a one. So this falls in the category of problems with calculus is easier than the algebra, so let&#x27;s look and see what we have. So I&#x27;ve got why Prime is equal to 16 temps, four x plus three cubed over X plus, one cubed, and then it looks like a minus three for X plus three to the fourth over X plus one to the fourth. And so now it&#x27;s just a matter of simplifying and see. OK, what can I do to simplify this? It looks like I can factor out for X Plus three cubed over X plus one cubed. So let&#x27;s do that. So I get why Prime is going to be four x plus three cute over X plus one. Cute. OK, so what? I&#x27;m factoring out is this cube term here in this cube term here? So that&#x27;s gonna leave me with a 16 and then when I factor out a for explosive three cube, I&#x27;m gonna have one left here and then one X plus one here, So I&#x27;m gonna be left with minus three four Expose three over X plus one. So now let&#x27;s just look at what&#x27;s in the parentheses and let&#x27;s combine this so this is equal to four x plus three cubed over X plus one cubed times. If you get a common denominator here of X plus one, then this becomes what 16 X plus 16 minus 12 x minus nine And so this is for X plus three cute X plus one cubed X plus one and it looks like I&#x27;m left with four x 16 minus nine is seven. So this final answer is four x plus three cubed times four X plus seven divided by X plus one to the fourth and that is it. So again, this, like that falls in the category of, you know, the calculus stopped right here. Okay. After the first step, I was done with calculus. It was just algebraic manipulation to get to that final answer and simplest form just dealing with rational expressions.

Karl Schaefer · Answer

and this problem were asked to find e drg s Where are is equal to sq two minus two s squared plus three. So we know that this is just going to be ah lim. The limit is h closes. You&#x27;re right. All derivatives are going to be limits. So where did each come in here? We need to plug in H s plus H to our function. So let&#x27;s just write our of s plus h minus R of s over age. So that&#x27;s the limit as H goes to zero of as plus age cubed minus two times as plus age squared plus three minus as cubed minus two. A squared plus three all over age. Let&#x27;s expand everything here. So, Albert, it&#x27;s a little bit messy. But don&#x27;t worry, it&#x27;ll it&#x27;LL work out pretty nicely in the end, let&#x27;s expand out to smell it over here as cubed plus three as squared H plus three. Ask H squared plus age cubed minus two. A squared minus four A. C. H minus two A squared plus three minus as cubed minus two s squared plus three all over age. But now we get some nice cancellations here. So we have an s cubed minus as cube. So that cancels. Here we have a minus two as squared canceling with a minus two s squared Cancel an A plus three minus plus three. So those cancel But now we see that we&#x27;re left with on ly h is here. So once we get rid of all these, you know, get rid of all these terms There&#x27;s a tsh is life that we can now cancel The h is so h on the bottom is going to cancel So this age squared becomes h the power of one cancel With this age, execute becomes a squared, a squared becomes age, Age goes away So now here it&#x27;s going to come up here We&#x27;re left with the limit as h goes to zero So now after we&#x27;ve cancelled all of the ages three as squared plus three as H plus H squared minus for s minus two age So these are the terms that were left with So here was thes these five terms Now we can just set eight people to zero when we get three as squared plus three times as time zero zero squared minus for s minus two times zero. So our final answer is three s squared, minus four s. So here is the derivative. This is DRG s where are was rescued minus two s squared, plus three.

Stephanie Martin · Answer

I&#x27;m a derivative are with respect to as you have to use the limit definition of the derivative, which is there in blue. I expanded our of s plus age before I started. I used the binomial theorem, um, to expand those. And then I distributed in the negative to as well. And we don&#x27;t have any, like terms. So, getting into this, we will have the limit. It&#x27;s as h goes to zero. So I&#x27;m going to put one over h times and then copy that down and then minus and then in parentheses, put, um, r s enclosed both of those sets of parentheses. And now what we have to do is distribute this negative here to all three of those terms. And then we are going Teoh, combine like terms soup. See? Okay. So we&#x27;ll get the limit as H goes to zero of one over age times once again, copy all of this and then minus s cubed plus two s squared minus three. All right, came saw these, like terms. Let&#x27;s see, minus s cubed plus s cubed minus two s squared. Plus two x x s squared and plus 3 a.m. minus three Okay, now, all the terms that are left, they all share a factor of each. And so I&#x27;m gonna factor that out so that I can cancel that h in the front, which is keeping me from plugging in that zero. So pull out that age and I&#x27;ll be left with three s squared. Plus three h s plus h squared minus for s my as to H and that&#x27;s it. My age is now. Cancel and I&#x27;m ready. Teoh, plug in that zero for H. So I will get three s squared, plus three times zero s plus eight groups plus zero squared minus forests minus two times zero. Which means that D. R. G s simplifies to be three s squared 00 minus four s minus zero. So then there is a

Hayden Woerner · Answer

all right, This is an exponential function. So the derivative three is just too coefficients was going to stay the way it is, and then we&#x27;re gonna take the derivative of the rest of this. So the derivative of four to the X squared plus two is four to the X squared, plus two times the derivative of X squared plus two, which is two x times the natural log of four. So just to reorder that, um, I&#x27;m gonna put the two in the three together to become six x times the natural log of four times four to the X squared, plus two.

Problem

Find the derivatives of the given functions. $$x …

Problem 32 Easy Difficulty

Find the derivatives of the given functions.
$$V=\left(4-\csc ^{2} 3 r\right)^{3}$$

Answer

$\frac{d V}{d r}=18 \csc ^{2} 3 r \cot 3 r\left(4-\csc ^{2} 3 r\right)^{2}$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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Anna Marie V.

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Precalculus Review - Intro

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$\frac{d V}{d r}=18 \csc ^{2} 3 r \cot 3 r\left(4-\csc ^{2} 3 r\right)^{2}$

Basic Technical Mathematics with Calculus

Catherine R.

Anna Marie V.

Heather Z.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Catherine R.

Anna Marie V.

Heather Z.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus