find-the-derivatives-of-the-given-functions-yfraccos-2-3-x12-sin-2-2-x-3

Question

Find the derivatives of the given functions.
$$y=\frac{\cos ^{2} 3 x}{1+2 \sin ^{2} 2 x}$$

Tyler Moulton · Accepted Answer

All right. We want to find Dy DX for the function. Why is equal to the coast Sine squared of three X divided by one plus two Sine squared two X. To do so, we&#x27;re going to rely on the road and shortcuts we picked up throughout single variable help particularly rule 033 With that here Roll zero is DDX in Mexico&#x27;s coast sex. Tv expose exploitative science rules one through three other power world product rule in general, respectively. If we write why in a more easily differential form, we&#x27;ll see how we can differentiate. Does he write why? As co squared three X times one plus two Sine squared two X 91st. Now we see how the derivative. It started off with the products that we proceeded. The derivative Dy DX is six coastline three extends to sign three X over one plus two Sine squared two X. This applies rules zero and three to co square three X minus coast squared three X times four signed two X times to co sign two X over one plus two Sine squared two X squared. This time we apply rule 0 to 3 again to one plus to sign to square two X two naked first, multiplying the first term. Buy one plus to sign two X over one plus to sign 22 X gives final solution. Dy dx is equal to six coastline three X sign three X one plus two Sine squared two x minus eight. Post square three X sign too exposed to X. All over one plus two Sine squared two X over squared

Philip Christensen · Answer

find the derivative of the function F of X, where X is equal to two all raised, or to race to the power of the quantity. Three plus sine X. Now we need to reboot one room off anything raised to the X exponential functions that he derivative anything of the form because of a to the to a function g of X, it&#x27;s equal to a to the G of x times, the natural walk of a then using the General Times cheap crime, his ex. So I can use this to solve for F prime. His acts are derivative of f of X, so we have that form. So we have 2 to 3 plus sign backs. That&#x27;s our G of X times natural log to then we need to take the derivative of G of X Year of axe sign packs. So our G prime of X is equal to three is a constant, so that goes to zero zero. Plus, he derivative of sign of X is co sign X. So then we multiply this by co sign hex that see derivative halfbacks

Amrita Bhasin · Answer

Okay. We&#x27;re gonna be deriving implicitly for this. So this means we have two x y plus x squared, Do you? Why? Over d backs equals d y o ver de axe clos de over de axe times x y sign axe plus X y coast Xanax. Okay, now that we&#x27;ve gotten this, we know we can write this as bringing the bottom. So I bring the right side on the left side because eventually we&#x27;re gonna be dividing by this that I&#x27;m writing in parentheses. Order to get the wild rejects by itself.

Sid Wan · Answer

number eighteen. We have y equals cause I lodge a log to Axe Cube. Absolute value. So still just good general collective. Sign off. That part has a lot to X cube, but fly directive off This part is one over to excuse. Yes, that&#x27;s his sign to execute to you.

Robert Daugherty · Answer

Section three. That six problem number 29 were daily with two first derivatives where you must use the chain role. So in this case, as everything in this math or capital is, it builds. So not only will I need to use the chain rule, I&#x27;m also going to usually use the product role to get some with an integrated. So why prime going to be equal to Let&#x27;s take that 1st 1? The product rules as take the derivative of that first portion two X times a signed Fourth of Eggs plus X squared. Now what&#x27;s the derivative of the sign to the fourth? That&#x27;s gonna be four times the sign cubed of X Times, the derivative of the sign of X, which is just co sign backs. OK, that takes care of the 1st 2 terms. OK, so that&#x27;s two X times signed fourth of X plus X squared times for signed Cube Co sign. Now let&#x27;s go to the next term. The derivatives of Ellicott that the derivative of X is just going to be one times co sign minus two of X plus. Then you&#x27;re gonna have X the river of co sign to the minus two is going to be minus two co signed to the minus three of X and then the derivative of the co sign is just minus sign of X. Make that a little bit smaller. Size fits, so it&#x27;s gonna be minus sign backs. Now, here again, we&#x27;re in the situation where calculus is all done. It&#x27;s just trig identities and algebraic simplification to see if we can get this looking any better. So why prime is going to be what two X signed, Fourth of X Um, plus four X squared sign cubed of X co sign of X and then it looks like I&#x27;m going to have a plus co sign minus two of acts. And then it looks like, um, plus to sign of x co sign minus three of X. Now, if you think about what you can do is I could say, OK, well, look at the 1st 2 terms. So why prime? I can factor out a two x sign cubed of axe, and then I&#x27;m left with sign of X plus two x co sign of X. And then if I look at these last terms, um, co sign to the negative too. That is the seeking squared of X Plus two. I can write this as the sign of X over the co sign of X and then times the secret squared of X. So now you see, you can factor out, um, a seeking squared of X. So when you do that, your final answer is going to be why prime is two X sign cubed of X sign of X plus two x co sign of X plus seeking squared of X and then you&#x27;re left with one plus two tangent of X. So here&#x27;s a case where, you know, you might argue it, but the the algebraic manipulation of these trick functions was more involved in the actual taking of the first derivative. Okay, so this is my final answer. You realize any of these would have been the right answer? Eso any of these is the right answer, but it&#x27;s just getting it down to the the final form that is the simplest

Maurizia De Palma · Answer

if this problem were asked to find the derivative of co sine squared of X and to make things a little easier, we can rewrite co sine squared of X is co sign of X Times coastline of X. And because we have two functions being multiplied together, we have to use product rule. So to find that we need to find the derivative of co sign of X so that can also be Britain as negative sign of x So now we can re rate Why? Prime of X as negative sign of X Times co sign of x close co Sign of X times Negative sign of X And when you simplify this, you get negative too. Sign of x co sign of X and this is a special double angle identity double angle. I don t so you can simplify this to negative sign of two x

Problem

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

Problem 26 Easy Difficulty

Find the derivatives of the given functions.
$$y=\frac{\cos ^{2} 3 x}{1+2 \sin ^{2} 2 x}$$

Answer

$\frac{d y}{d x}=\frac{6 \cos 3 x \sin 3 x\left(1+2 \sin ^{2} 2 x\right)-8 \cos ^{2} 3 x \sin 2 x \cos 2 x}{\left(1+2 \sin ^{2} 2 x\right)^{2}}$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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$\frac{d y}{d x}=\frac{6 \cos 3 x \sin 3 x\left(1+2 \sin ^{2} 2 x\right)-8 \cos ^{2} 3 x \sin 2 x \cos 2 x}{\left(1+2 \sin ^{2} 2 x\right)^{2}}$

Basic Technical Mathematics with Calculus

Catherine R.

Kayleah T.

Samuel H.

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.

Samuel H.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus