find-the-derivatives-of-the-given-functions-y6-cos-1-sqrt2-x-3

Question

Find the derivatives of the given functions.
$$y=6 \cos ^{-1} \sqrt{2-x}$$

Tyler Moulton · Accepted Answer

we want to find dy dx the river Y. With respect to X. For the function. Why is equal to six? Our coastline of route two minus X. In this problem, we need to rely on the rate of shortcuts that we picked up through a single variable calculus in particular, we need to use our newly learned inverse trig and metric derivatives. So I have listed here the three major inverse trig derivatives. In particular. We need to use that. DDS arcos X equals negative one over square root one minus X squared. Since the argument of our coast is square root two minus X. Were also we need to make use of the chain rule, which we&#x27;ve learned before to solve this so we can rewrite why as six our coast to minus 61 half. That makes it easier to see how the chain will gets used in the argument. Our coast. Thus we have our derivative. Do I. D. X equals negative six over square root one minus two minus x square times by chain rule driven. What&#x27;s inside parentheses? Or our coasts? One half, two minus X, negative one half times negative one. Thus are negatives cancel. We multiply our constants out and we shift our two minus X, the negative one half of the numerator denominator to obtain solution three over square root two minus X times x minus one.

Sid Wan · Answer

okay. We want to find the derivative off, dysfunctional. Why? Cause selective consigned to explore us? Cause I Hi over six. Why private? Because this party is a constant, right? This a lumber. There&#x27;s no blur but there. So you got just equal, Cyril. And you take a deer of so just this part consigned to X Now that you&#x27;ve signed to excite to act, multiply his far directly with two channel to assign to X.

Ernest Castorena · Answer

they give us the curve defined by the equation Y squared, is it? What? Excuse mine. It&#x27;s exciting plus for coastline white, and they want us to find the second derivative. So it&#x27;s go missing and you train wrong to Why times? Well, that area of the inside of my brain. The sequence of the X Square minus six plus for it, minus workers It&#x27;s negative Sign minus for sign of white times. Why prime all of that times like him. And now we can bring our lifetime terms to the same side. So we&#x27;ll have to want clothes for sign of wine you want to find my way is equal to three X squared minus six. Let&#x27;s take our second derivative now. Well, it&#x27;s easy to get only one term with wide double room. So Well, huh was predictable. My primetime. This factor alone for Sign White, now of the UAE, prime alone and take the narrative of ah coefficient away from which is two y prime bus for co sign of what times like Graham and all that is equal. Teoh. Well, let&#x27;s say six X and then the constant drops. So we have why prepper times this coefficient. Teoh. What&#x27;s force? I know it is equal to you. It&#x27;s exciting. My nets. Why prime times to I prime Plus why crime for coastline white We have backdrops that life family Yeah, I m squared on the front lines again, all over to white but it&#x27;s for a sign. What way? That on both sides. Let&#x27;s actually factor out. Oi Prime Time to make it a little simple. Good. And then make a wife prime stare Square it over again. Well, this second derivative has been around what can get it purely in terms of x and y by what was on the cell to write. Pramuk, you&#x27;re already where we got the X squared minus six. We can divide both sides by Teoh Plus for a sign white. And then if you wanted to get it really in terms legs and I could take this expression, we&#x27;ll get in here so you square it, multiply it out and they

Theresa Nguyen · Answer

we&#x27;re looking for the derivative of Why is equal Teoh Negative X cubed coastline of X plus three X squared sedative X plus six x co. Sign of eggs minus six sign of x To solve for this, we&#x27;re going to use thes sub difference rule to break down our derivative Be some difference. Rule is F plus minus G prime is equal Teoh f prime plus minus cheaper Applying this rule are derivative Will look like minus D over dx of x cute co sign X plus de over T x three X squared Sign of ass plus D over DX of six co sign of X put minus de over D X of six Sign. Relax. So now we went to start solving for all of these derivatives We&#x27;ve broken down starting with D over DX as ex cute co sign X to solve For this derivative, we would to use the product rule f times G prime is equal to ask time terms Jeep plus f times g prime here are s is equal to x huge So our f prime will be three x squared RG is coastline of X so our G prime will be negative side effects Putting it all together We will get three X squared co sign that X plus negative sign of X Well supplied by X Cute simplified that will look like three X squared co sign of X minus X cubed site of X This is one derivative down. The next derivative will be D over DX of three X squared site of acts to find this derivative were also using the product rule here R f is s squared so our f prime will be to S R G is side of X so I keep time will be co side of X putting use. Together we will get three multiplied by two x sign of X plus co sign of X terms X squared. Our next derivative will be D over DX of six x co side of s. To do this, we use the product rule again. So our f is X last time will be one RG is co side of X So our g prime will be negative side of X Putting these together we will get six times one times coastline X close, negative sign Look x Times X. Now we&#x27;re going to put all of the derivatives we&#x27;ve taken together, which will be okay. Negative. Three X Squared Co. Sign of X minus X cute side of X plus three times two x sign of X Plus Co sign the X Times X Squared plus six co. Side of X minus six. Sign of X. Let&#x27;s just take this down. Co spin of X minus six Sign of X minus six co side of X. If we take all of these and we simplify, we will get X huge sign of 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.

Gilbert Deleon · Answer

we&#x27;re gonna take the derivative of this function six over the fourth root of X. To take the derivative of this function, we&#x27;re going to use the power rule which is the derivative of X to any constant exponents, Um is multiplied by the exponents and then decrease the exponents by one. So that time we would take the derivative of the power function. Before we could do that, we need to write this function as a power function. So one thing that we can do is we can rewrite the fourth route as a fractional exponents, ext with 14 and then another thing that we can do this. We can rewrite that positive exponents in the denominator as a negative exponents in the numerator. And now that we have this in a power function form, now we can apply the power function rule to differentiate. So we have a differentiated yet we&#x27;re different shading now before we&#x27;re just rewriting in terms, rewriting our function as a power function. Now I can multiply by the exponents, so it&#x27;s gonna be six times negative. 14 negative, six over four and then decreasing the ex opponent by one&#x27;s negative 1/4 minus one. Uh, subtracting fractions, getting a common denominator, It&#x27;s gonna give us a negative force. So then, after we differentiate now, we can do some simplification. The derivative D y the eggs, bacon simplifying six over four to be three house and then excellent. Negative. Five over four. And then something else we could do is we could rewrite that negative exponents a za positive exponents in the denominator. And I want other thing that we could possibly do is we could rewrite that fractional ex opponent as a route. You were right that factual exponents as a route that fractional extra only applies to the X will be two times before through of X to the fifth.

Problem

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

Problem 9 Easy Difficulty

Find the derivatives of the given functions.
$$y=6 \cos ^{-1} \sqrt{2-x}$$

Answer

$\frac{d y}{d x}=\frac{3}{\sqrt{x-1} \sqrt{2-x}}$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Kayleah T.

Caleb E.

Kristen K.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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$\frac{d y}{d x}=\frac{3}{\sqrt{x-1} \sqrt{2-x}}$

Basic Technical Mathematics with Calculus

Kayleah T.

Caleb E.

Kristen K.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Kayleah T.

Caleb E.

Kristen K.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus