find-the-derivatives-of-the-given-functions-ytan-1ln-2-xln-x-2

Question

Find the derivatives of the given functions.
$$y=	an ^{-1}(\ln 2 x+\ln x)$$

Tyler Moulton · Accepted Answer

Yeah we want to find dy dX four. Why is equal to the arc tangent of natural log when the two X plus natural log Ln X or L N X. So to solve this, we need to have an understanding of differentiation shortcuts for transcendental functions in particular logarithmic functions. So we noted relevant rules below zero on the left is dB X log bu equals whenever you log E D X D X L. Any was defined similarly on the right. We have the power world product will in general, respectively. Why has already written it&#x27;s most easily defensible form. So we can proceed to solve we don&#x27;t have to use the chain rule involving first the derivative of art tangent of Ln two X L N X. Then we&#x27;ll use real zero on the contents Ln to expose Ln so you I d X is 1/1 plus Ln to expose Ln X square. This is the derivative are tangent, Hampton Inn and what&#x27;s inside which is to over to expose one over X. One of the experts, one of rex&#x27;s two over X. So we have solution to over X plus X times Ln two X plus L n x squared.

Sid Wan · Answer

Columbia, twenty. Why goes Lancelot ofthe tent square? That&#x27;s absolutely where you live. Peron equals so natural love of something. The one hours after. But fly this car derivatives, which channel and you use general again to attend acts? What clock? Derivative ofthe tent exits back X square. And you can&#x27;t cross one of those two seconds. That&#x27;s where forward ten looks.

Kathryn Stefanko · Answer

So if we have a function such as f of X equals two x times tangent inverse of X minus Ln of one minus X squared and we want to find the derivative of this function, this is a bit of a longer function and will require multiple types of derivative rules. So looking at the first portion of this function, we noticed that we have two x times tangent, inverse of X, so that because of that multiplication, there&#x27;s gonna be the product rule. So I&#x27;m just gonna identify with one line that I have my two x first and my tangent in verse second. Then there is a subtraction and we can move on to the next portion. And we have log rhythm, which is gonna be the derivative rules for log rhythms. So I identified that I have a log rhythm, and I also identify what the inside of that is now just to write this out all in one line with the rules for how this is going to work refined the derivative of F of X is gonna equal two x times the derivative of that tangent in verse of X. We&#x27;re not done with the product will yet because it&#x27;s the first time. So the derivative of the second plus the second operation times the derivative of the first So tangent inverse times d d ex of two X. Now we&#x27;re done with that first portion and moving on to that log rhythm. The rule for log rhythms is that for L. M. For the natural log rhythm, and by the way, that minus isn&#x27;t a rule about the derivatives. It&#x27;s just because that&#x27;s how it is in the original function. So finding the derivative of the log rhythm that means it is one over. Whatever the insight is, which is one plus X squared times, the derivative of that inside, which is one plus X square. Now actually finding the derivatives, I&#x27;m plugging them in. I have my two x times. The derivative of tangent Inverse is something we usually get with a table. It is one over one plus X squared. Then I have plus tangent in verse of X times, the derivative of two X, which is to minus 1/1 plus X squared times, the derivative of one plus X squared, which is just two X. Now here you should notice that what you have is to x times one over one plus X squared and then later, minus 1/1 plus X squared times two x. This is the same value as this, and I end up subtracting it. So in my final answer, all I&#x27;m gonna be left with is to tangent inverse of X, and that would be my final answer.

Philip Christensen · Answer

given the equation f of X equals X squared, plus one times the natural lager X. We need to find the derivative of this function. So to do that, we need to start with the product because we have two functions here x squared plus one of the natural log decks. So the product rule for a quick refresher for two functions G of x and h of X multiplied together the remove that over the axe of that is equivalent to G of X plans h crime X waas h of x climes G crime of X So we can start with the X squared plus one as our g of X just move up just a little bit. Not till ports Thank you technology and we can label this Sergiev X to label natural law is our Agent X now using this, we can first saw for G of X x squared plus one. So we get crime of X equal to G of X. So that&#x27;s squared plus one times the natural times the derivative of the natural lock text which is just one over X plus the natural log backs These times the derivative of X squared plus one. Now, since one is a constant, that would be that will go to zero, and the derivative of X squared is brightness below since we need to use it for the power. So X ray still power derivative of that his ex to the and were actually in power X tax, um, equals 10 times X to the n writes one. So in our case, we have two times X to the Tu minus one. So that&#x27;s just one. And we can leave that export out. So that is it. You could simplify this multiplying out, but I think it is cleaner than this current stitch.

Todd Vawdrey · Answer

Okay, So this problem, we&#x27;re finding the derivative of the tan squared X. So we&#x27;re gonna have to go ahead and apply the chain rule right here. Structurally, we have the tangents of ex inside of a squared function. So we&#x27;re gonna have to first do the squared. I&#x27;m using the power rule. So the two drops down and then we keep what the input waas. And then we need to multiply it by the inside of the function, which is that tan X and derivative of the tangent Is the C camp squared so altogether the derivative is to 10 x c can&#x27;t squared X.

Linh Vu · Answer

given the function, why go to x times? They want goji land off X squared plus four minus x times tension in those off of a Jew and there wasn&#x27;t asked to find a wiper him. Now do the first time here because we have the airline. So my former fund And then we should get in the denominator where exactly? The X cameras for and by the general we need to apply. And that X squared plus on the riveter on the top. And now for the second term here we have your blind a product rule here because we have two functions so year times you Tim&#x27;s video negative which getting quickly you Prem v Bless you, big prime. So we applied this formula for the product Where we get now will be next prime times tension in verse of the Expo over two and now doesn&#x27;t minus away used. We can disagree the madness inside, So I will have a minus 10 s quell X times that luncheon inverse under X over it. You derivative Here the next time we need Teoh complete the terms that having the derivative new so we can do undersigned now on the X Square, my plus for derivative the literary three of the extract two X and the derivative the foreign coaches zeros on the Now the next one will be on We have the X business wondering one What did you do? This one is that Yeah. So express m where you could you want It&#x27;s very obvious And now the last one will be tension in verse of the Exxon But you iRiver tive so by the formula for the rift over inverse function which you get to go to the X on with you You negative divided by one minus X on with you square That&#x27;s a family fun attention in verse and now for this one And they lived in the X and Y Jr brand illiquid your half If I have the one on which black and write it down here now when my house exclaimed of a phone and we can certainly find this one and then we get one day running by this one will be tu minus. Now, uh, to when it&#x27;s the X squared over four over true additional B, plus my path we can register is the can gonna do the common denominator here. So have a true off far plus X square, So ever be Sit on, then we can certainly find it on. And then we get for this one again. The two x of ah, ex glamorous for no minus. Attention involves. I&#x27;m the Exxon, but, you know, minus we have the X on the top. Yeah, but this one together, so have that you x over x squared plus four. We say that this one and this one can be cancelled now because they&#x27;re exactly that. Form the one prime when you go to, and we will have the, uh, minus the dungeon. Inverse. I&#x27;m the expert with you on, that would be the answer away from

Problem

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

Problem 24 Easy Difficulty

Find the derivatives of the given functions.
$$y=\tan ^{-1}(\ln 2 x+\ln x)$$

Answer

$\frac{d y}{d x}=\frac{2}{x+x(\ln 2 x+\ln x)^{2}}$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Catherine R.

Kayleah T.

Caleb E.

Joseph L.

Precalculus Review - Intro

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$\frac{d y}{d x}=\frac{2}{x+x(\ln 2 x+\ln x)^{2}}$

Basic Technical Mathematics with Calculus

Catherine R.

Kayleah T.

Caleb E.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Catherine R.

Kayleah T.

Caleb E.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus