find-the-derivatives-of-the-given-functions-y3-cot-6-x-3

Question

Find the derivatives of the given functions.
$$y=3 \cot 6 x$$

Tyler Moulton · Accepted Answer

mhm. We want to find the derivative. Why with respect to X. Dy dx for the function Y. Equals co Tandy xxx to do so. We&#x27;re gonna rely on derivatives shortcuts we picked up throughout our journey and single variable count. So most relevantly we&#x27;re gonna make a note of the trigger metric derivatives. These are D. D. X in X equal co sex DDX co sex negative sine X. D. X. 10 X equals decant square DDX co tangent X. Equals negative Costa can&#x27;t squared and so on. We also make note of the chain rule product rule and so on. Other derivative shortcuts we&#x27;ve learned particularly for this problem. We need the derivative of tangent combined with the chain rule so we can rewrite as Y equals recruit and sex. That is our function is already the most differential form for the most easily defensible form. So dy dx is three times negative coast. Can&#x27;t square six X. Is the tip of koh tangent. We multiply by six by the chain rule on six X. And give us a final solution. Dy dx equals negative 18 times coast. You can&#x27;t squared six X.

Todd Vawdrey · Answer

where this problem we&#x27;re finding the derivative of negative six extra. The fourth sign. Six sects. For this, we&#x27;re gonna need to do the product rule. So I have two functions being multiplied together. We have the negative six x to the fourth, and then we have the sign of six X. So for the product rule, we&#x27;re gonna go ahead and get that D y d x is equal to we take the derivative of the first, which is negative 24 x cubed times The second sign six x plus the first thing negative six x to the fourth times, the derivative of the second, which is the co sign of six X. And then we multiply that whole thing by six because of the chain rule and the derivative of six exes. Six. So then we can go ahead and simplify this thing. So you get negative. 24 X cube signed six x. I&#x27;m gonna put the sixes together minus 36 extra. The fourth co sign of six X. You may also see this factored so they have a common factor of negative 12 x cubed. And then what would be left if I kept that is signed to the six X Plus three ex co sign six x So you may also see it like that, depending on your teacher, but they&#x27;re both correct.

Alex Roush · Answer

Okay, so we have to find the derivative of this immediately. We see the product of two functions. So, product, it&#x27;ll kind of screams at us now. In the past, whenever we multiplied to polynomial is together, we actually went ahead and expanded it out and discovered that taking the derivative of that was usually easier. But because this is called a transcendental function, it&#x27;s an exponential. Combined with the polynomial, The product rule really is the best way to go. Okay, so f prime of X is going to be the first function times the derivative of the second. Okay, So since this is a polynomial, the product rule applies here. The power roll place. So I&#x27;m gonna take these exponents, bring them down his coefficients. Okay, so this would be three acts, and then I&#x27;m gonna decrease the exponent by a factor. One a three minus one is to okay. And then I&#x27;m gonna bring this sex, put it down as a coefficient. So I have three times 2 to 6 x to the first power. Okay. And this is linear. It&#x27;s looked at six. And then the derivative of a constant is zero. Now I take the second function, and I multiply all this times the first, the derivative of the first function. But the derivative of the exponential is just the exponential. It&#x27;s no what I&#x27;m gonna end up having if I simplify this little bit, I mean a factor in each of the X out. And I get what? Well, have one x cubed trim. Okay, I have this minus three acts in this positive three X that are gonna cancel. Have this negative six sex in a positive six sex, which are also gonna cancel. And I have a negative six and a positive six that also cancel. So everything cancels except the sex que term, which is really nice. So that&#x27;s your answer.

Gilbert Deleon · Answer

we&#x27;re going to determine the derivative of dysfunction six X squared minus 10 X minus three X to the negative, too. To differentiate this function, we&#x27;re going to be differentiating terms being added or subtracted. And so that is this rule when I want to differentiate terms added or subtracted Ah, differentiate turned by term. And we&#x27;re also gonna be using the rule for different Jane and power function, which is extra constant exponents. And the way that I differentiated power function is I multiplied by the exponents and I decrease the exponents by one. So then differentiating term by term, it&#x27;s going to give us the derivative D Y. D. X has equal to multiplying by the exponents for the first time. Six x squared. He&#x27;s gonna give me 12 X decreasing the exponents by one gives me to the first power minus the derivative of 10 X, which is just 10 and then for the last term, multiplying by a negative too is going to give me a negative six. So we&#x27;re subtracting the negative six and then decreasing that exponents by one is gonna give me a negative three negative to minus one gives me a negative three and then thinking about how we can rewrite this is gonna give me 12 X minus 10 plus six x of the negative three minus a negative becomes a plus and then six over that. Negative exponents weaken right as a positive exponents in the denominator.

Smita Praharaj · Answer

in this question, we are asked to find the derivative off. Why equals six over X rays to the four minus two over X Cube plus five over X plus square off three. Now we can ride this as six times X rays to the negative four minus two times X rays to the negative three plus five times X rays to the negative one plus square off three. Now we know that the derivative or some or difference off functions the same as some are difference off their derivatives. So D Y over DX becomes dd X off six X rays to the negative four minus dd x off to X rays to the negative three plus dd x off five X rays to the negative one plus dd x off square off three Now in the derivatives here, six, two and five are constants, so I can pull those out off. The derivative on DH square of three is a constant, so this derivative equals to zero. Okay, now divide over DX equals six times the over DX off X rays to the negative four minus two times dd x off X rays to the negative three plus five times dd x off X rays to the negative one. Now we&#x27;re going to use the power rule to find the derivatives. We know that the power rule states that ddx off X rays to the end. Where and is any number is n times X rays to then minus one. So hear my ends are negative for negative three and negative one, So that equals six times negative. Four X rays to the negative four minus one minus two Negative three times X rays to the negative three minus one plus five Negative one X rays to the negative one minus one. Now six times negative for is negative. Twenty four X rays to the negative four minus one is negative. Five. Negative two times negative. Three ISS plus six X rays to the negative three minus one is negative four. Five times negative one is negative. Five X rays to the negative one minus one is negative, too, so that&#x27;s the derivative off the function. We can also write this derivative as negative attorney for over X rays to the five plus six over X rays to the fore minus five over X square

Matthew Allcock · Answer

in this video, we&#x27;re gonna go through the answer to question number 13 with a 7.3 for us to find the motive. Why is equal to X? Sorry to proceed with 6/10 lunch X over three. So do I. The ex. Well, the six is just a constant you can keep. I keep six. Ah, son of ex Differentiate Kash. Next. But it&#x27;s excellent. Three. Keep that inside and then using the changeling, we&#x27;re also gonna differentiate most part by the derivative off the inside, which is a bed for the third. And the sex is gonna so to make two. Gosh, excellent.

Problem

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

Problem 6 Easy Difficulty

Find the derivatives of the given functions.
$$y=3 \cot 6 x$$

Answer

$\frac{d y}{d \theta}=-18 \csc ^{2} 6 x$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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Precalculus Review - Intro

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$\frac{d y}{d \theta}=-18 \csc ^{2} 6 x$

Basic Technical Mathematics with Calculus

Anna Marie V.

Caleb E.

Michael J.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Anna Marie V.

Caleb E.

Michael J.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus