find-the-derivatives-of-the-given-functions-y2-ln-tan-2-x-3

Question

Find the derivatives of the given functions.
$$y=2 \ln 	an 2 x$$

Tyler Moulton · Accepted Answer

mhm. We want to find the derivative dy dx for the function. Why is equal to two natural algorithm of tangent of two X. This question is testing our knowledge of differentiation shortcuts, particularly those for transcendental functions and even more specifically for logarithmic functions as such as defined the relevant rules for director of taking on the left. Our rules zero DDX log you into the Excel interview on the right. We have the power rule, product rule and chain will respectively. And this problem leading to use multiple zero and three the chain rule to solve so Y equals to Ellen tangent of two. X is already in its most easily defensible form and that&#x27;s probably going to use dD Exelon. U equals one over you. D you D X for U equals 10 2 X. So we proceed to solve the U i d x is two times one over you won over 10 2 x times du dx. Which is he can&#x27;t square two X times to buy the chain rule. Simplifying this expression gives us dY dx is equal to four times a C. Can&#x27;t squared of two X, divided by the tangent of two X.

Bobby Barnes · Answer

We want to find the derivative of why, too next, plus one times exposed to over X minus one times X minus two so we could use a combination of the quotient and product. Rule two takes derivative. But if we just do a little bit of algebra weekend, simplify the numerator and denominator to the following. So the numerator we can expand to give us X squared plus three X plus two that are along there becomes X squared minus reacts plus two. And so taking the derivative of this will be application ofthe question. So let&#x27;s go ahead and write out what the question is. So the cushion rule is if we have the derivative of DX, and so I have to fight it out using this jingle, because otherwise I please forget something or put something on, please. So I&#x27;m going to write says hi over Lo&#x27;s. Our new Maria is going to be high and our home there&#x27;s going to be looking so terrific. Do or the crucible will be so it&#x27;s low D Hi minus Hi Steve O and call over the square of What&#x27;s the look? So you couldn&#x27;t make this using F&#x27;s and Jeez if you want. But I really do need to save the world. You go every time. Otherwise something gets misplaced without though, So we want to find the derivatives. It was gonna be y prime, and I&#x27;m going to write everything in the same color just so we can keep track of everything. So ddx Oh, so are numerator is going to be blues though x squared plus three x plus two over our denominator expert minus three x wass too. So this derivative here So it&#x27;s low. So x squared minus three x plus two times the derivative with respect to x o what we have in the numerator x squared plus three x plus two And then we subtract off than in the ops ID or so Now we write X squared plus three x plus two and we multiply by the derivative of the function in the denominator X squared minus three x plus two And then you divide all this by what you have in this dominators X squared minus three x plus two square. But, you know had actually with that in the correct color, so should be green. So x squared minus three X plus two. So something I&#x27;m going to do just to save a little bit of time and space is so knows that both of these air quadratic they look essentially saying So what if we tried to take the derivative of this? So the only thing actually differs is our middle term here. So I&#x27;m going to write this the derivative with respect to x o X squared plus B X plus two. Since our middle term is the only one that is actually changing so we can go ahead and use the sum and constant property to rewrite this as the ex X squared plus b tvx Thanks Wass ddx of two now first derivative of a constant is always zero. So we just go ahead and write that. And then taking the derivative of X squared will be power rule. So it&#x27;s moved to outfront subtract off one. So the two times ex first power believe only don&#x27;t write power of one. So I&#x27;LL go ahead and just and then X has a power of one to it so we can move that out front extracted off. So plus B times one and in fact, to be zero power. But anything is there, a power will be one. So we don&#x27;t need to write that one either. So these gorillas will be two x plus whatever the middle terminus. So this derivative here will be two x plus degree and distributed here will be to X minus three. Now, let&#x27;s go ahead and let&#x27;s actually oil this out so it&#x27;s gonna be kind of long. So hopefully it all in our space doing this so X squared times too, will be to execute Explorer. Times three will be plus three X squared, minus three x times two x will be negatives squared and then times three will be minus nine X Now two times two x will be four X and then times three will be six. All right now we need to subtract off when we multiply these other two together. So we have first Thanks. Let me go ahead and actually move a little bit because it looks like it&#x27;s getting late. So X squared times two x again will be too cute. Minus threes will be minus squared and plus three times to actually be plus six packs and the three X times minus three will be negative nine x and then plus two times to expertly cross or X and then two times through minus six. And then all of this still over our denominator Expert minus three x plus two squint. Now let&#x27;s go ahead and start collected terms. So since I&#x27;m subtracting this expression in parentheses, all the signs will be flipped. So first notice, I have to execute tier and to execute in here. So those council of Let&#x27;s see what Constance. I&#x27;m on minus nine x here and Maya Sonics. There&#x27;s of those Sam sloped hi love for X here and a for ex hears of those to cancel out. And then the rest of these are just will be the same thing added to itself. So looks like this the time, and and let me go ahead and draw little barrier like this. So everything that I actually have on the left side will be doubled. So we could write this as six x squared minus twelve ax squared plus twelve all over X squared minus three x plus two squid. And this here will be our final Oh, actually, Hello. Hello Myself? No, we have some squared So why don&#x27;t we go ahead and combine those? So actually we can write. This is negative six X squared plus twelve all over. Expert minus three X plus two square. And then once we do that, you might remember that our denominator wass X minus one and ex wives too. So let&#x27;s go ahead and we write it like that. Those x minus one and then it will be squared X minus two squared since it&#x27;s quiet there and our new radar will affect her so we can perspective on the negative six and we&#x27;LL end up with X minus or X squared minus s two. And we can&#x27;t really simplify this any further, but at least we have it in this nice looking factor for so we could either leave or answer like what we had over here or in this nice factor. Four

Sid Wan · Answer

can number ten. Why? Because to ACS that why prime vehicles products of product rule to multiply sack for X plus to ask somebody about this party rooted is suck Ex directive is sek full expand for export cry directive off for exit four So simplify equals a hand but by a sack full expense four.

Runpeng Li · Answer

so four problem seven function were given. Here is why today, why is equal to two times X cube so B y d X? That is a derivative of dysfunction? We&#x27;ll be three times two. That&#x27;s six coefficient and the power will be three minus one. So that&#x27;s two, and this is

Stephanie Martin · Answer

Okay, let&#x27;s find the derivative, Um, of why equals two X cubed. Using the limit definition of the derivative, um, we will get the limit as h goes to zero of why of x plus h, which I expanded up there using, um, the binomial theorem and then distributing in the two. That&#x27;s the quickest way to do it. Um And then also, I&#x27;m gonna write this as one over h times and then two x cubed, plus six each x squared and then minus Why so minus two x cubed, no thes cancel and then notice every term. Now hasn&#x27;t each left in it. So I&#x27;m going to factor that out. Now. These ages cancel, which was my objective. And now I can plug in that zero for age. So then I end up with six x squared, plus six times zero times x plus two times zero squared. Which means that D Y d eggs or the derivative of y with respect to X is equal to six x squared. And that is it

Amy Jiang · Answer

Okay, so let&#x27;s take our fallen derivative. So we see that we have the natural law started to a bit of that, um, that people to one over our inside, which is hyperbolic speaking to ex. And now we want to take the derivative of our inside, which is the derivative of hyperbolic seeking about secrets. And they&#x27;re gonna are both sickens of to and then hyperbolic tangents of two X and then taking the derivative of that inside just to acts that people todo So we get negative to defeat it. He&#x27;s to cancel, and we&#x27;re left with hyperbolic tangent. Do that.

Problem

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

Problem 9 Easy Difficulty

Find the derivatives of the given functions.
$$y=2 \ln \tan 2 x$$

Answer

$\frac{d u}{d x}=\frac{4 \sec ^{2} 2 x}{\tan 2 x}$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Grace H.

Anna Marie V.

Heather Z.

Caleb E.

Precalculus Review - Intro

Functions on the Real Line - Overview

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$\frac{d u}{d x}=\frac{4 \sec ^{2} 2 x}{\tan 2 x}$

Basic Technical Mathematics with Calculus

Grace H.

Anna Marie V.

Heather Z.

Caleb E.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Grace H.

Anna Marie V.

Heather Z.

Caleb E.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus