find-the-derivatives-of-the-given-functions-y4-x-sin-3-x-3

Question

Find the derivatives of the given functions.
$$y=4 x \sin 3 x$$

Tyler Moulton · Accepted Answer

All right. We want to find Dy Dx for the function. Y equals four X. Signed three X. So we&#x27;re going to rely on derivative shortcuts. We picked up a single variable cut this all, especially those relating to training metric functions. So the most relevant rules are listed here. Rule zero G D X in Mexico&#x27;s Cossacks. Tv expose expos negative syntax rules one through three are the powerful product rule and general, respectively. We&#x27;re going to rely on all four of these rules to solve this particular derivative. So first Y equals four X and three X is already in the most easily form to differentiate. So we proceed straight to the derivative so we have derivative as follows. Dy dx is equal to four signed three X plus four X. Coast three X times three The terms and left and right are separated because of the product rule on the left. We apply the power rule for four X on the right. We apply we&#x27;ll zero in the chain rule to turn sign three X in the coast. Three extends three. Thus be a final solution. DY DX is equal to four signed three X plus 12 X times the co sign of three X.

Shumayal N · Answer

for more complicated functions like these, you start with the derivative of the outermost function and you work your way in. So the derivative of sign, which is the outermost function, is cool. Sign and you write the inter function as it ISS for X cubed plus three eggs, most one. And then you take the derivative of Thean Er. Function separately so we&#x27;ll do D over the X or X cubed plus three eggs plus one. Now the derivative of four X cubed is going to give us four into three X squared. The derivative of three eggs will give us three into one and the derivative of 10 Hang. Do you already have call sign or ex cute? I love three eggs plus one, which give this our final answer of love. X squared plus three well supplied room Total sign oh or execute plus three x plus one

Heather Zimmers · Answer

Here&#x27;s a composite function that we&#x27;re going to differentiate using the chain rule and the good news is that even though there are going to be a lot of steps because we have a lot of layers in this composite function, there&#x27;s not going to be any simplifying. Weaken do and we&#x27;re done. So that is often a relief because the simplifying is usually the most complicated part of the process. So let&#x27;s find the derivative notice that the outermost function is the fourth power function. So we bring down the four and we raised the inside to the third. So we just write the entire inside over again. But now it&#x27;s to the third. Now we multiply by the derivative of the inside. So just focusing on this part, which is a some and the derivative of the sum, is going to be the some of the derivatives. So the derivative of X is one plus. Now we&#x27;re finding the derivative of this inner part, and we&#x27;re going to need to use the chain rule on that. So we bring down the three and we raised the inside to the second. Then we multiply by the derivative of the inside, and the inside is a some. This part here is a some and so it&#x27;s derivative will be the some of the derivatives. The derivative of X is one plus. Now we need the derivative of sine squared X, and remember that sine squared X means the sign of X quantity squared. And so it&#x27;s derivative would be, according to the chain rule, two times a sign of ex because you bring down the two and you raise sign to the first multiplied by co sign of X because that&#x27;s the derivative of sign. So that&#x27;s what we have next to sign X Co sign X. Okay, we made it to the very inside and then we look at that for a minute and we ask ourselves, What can we combine? What can we factor out? And we realized that because of the plus signs, primarily it&#x27;s kind of stuck the way it is. So there you have it

Sid Wan · Answer

number twenty six will define the derivative off. Why Wass Science three acts plus Coast Coat Coat, X coat hand execute with Ace So first we take this as a oh ho ho. It&#x27;s eight off this part. It&#x27;s Cube servants says this power, and we have to multiply derivative off. What&#x27;s inside? So your own people first, this part is going to be co signs for excellent blustery channel Klaus coat hands. Ex Directive is and collective Call C can&#x27;t Max Cube Square multiply derivative of Tex Cube. So relax squared channel. So even assemble. Devise a signs of post co tenant execute Sellards by three, cause I Thrax liars throughout square Cosi because he can&#x27;t execute square. Yeah, that&#x27;s it. Just used power and general inside work for this one.

Louisa Benatovich · Answer

What is the derivative of f of X equals for sine X minus X. Whenever you see a plus or a minus sign like you do here, you couldn&#x27;t split it up into two sections, so we have the floor sine x and then we have these minus six. Let&#x27;s look at the first section underlined in blue. We&#x27;ve got a chicken a metric derivative. So you&#x27;ve got to remember that the derivative GDX Senate thing equal to co sign thistles. Just something you&#x27;ll have too much. So when you&#x27;re doing good derivative, you take this. This is just a constant. Bring it down, It doesn&#x27;t change. And then you just plug in your coastline X because the sine X becomes coast perfect. How? Look at the other side. This is just power. Will you see, Noble for the derivative of negative X would just be negative one. So your final answer is f prime of X equals four co sign next minus one

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

Problem

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

Problem 15 Easy Difficulty

Find the derivatives of the given functions.
$$y=4 x \sin 3 x$$

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

Grace H.

Heather Z.

Caleb E.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

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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

Grace H.

Heather Z.

Caleb E.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Grace H.

Heather Z.

Caleb E.

Michael J.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus