find-the-derivatives-of-the-given-functions-y3-sin-1-x2-2

Question

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

Tyler Moulton · Accepted Answer

we want to find the derivative dy dx for the function. Why is equal to three times the arc sine or inverse sine of X squared? This question is testing our knowledge of the different differentiation shortcuts that we picked up throughout our journey. And single variable calculus in particular, it&#x27;s testing our knowledge of the newfound derivatives for inverse trig identities or for inverse trig functions. So I listed all three inverse regular this year. In particular, we need to use that DDX arc sine X is equal to one over the square root of one minus x square. We combine with this with the chain rule to solve for this derivative. So why equals three arc sine X squared is already in its most easily differential form so we can proceed differentiate. Thus we have, Do I react equals three Times. Are the General two X over one minus x squared squared square rooted or simplified? Dy dx is equal to six X divided by the square root of one minus x to the fourth.

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

Todd Vawdrey · Answer

Okay, so this problem we&#x27;re taking the derivative of y equals negative three e to the to sign X. So this is a composition of functions or have this function right here inside of a negative three e to the X function. So the derivative using the chain rule is just going to be the outside funk, the derivative of the outside function, which is three e to the to sign X times the derivative of that green function which is to co sign X so all together we can go ahead and write that as negative six e to the to sign ex co sign X oh.

Ernest Castorena · Answer

for this question. They want us. It&#x27;s sign explained is equal Teoh X squared minus Think they want us to computer Literate of a wind Find in the situation invisible So let&#x27;s see grinding Teoh General for this Well, uh, think of the derivative with respect to X Well, how coastline, Uh, excellent. The rear of the inside which will need the product. So nobody with the first factor leave the second alone. It&#x27;s about sex. And then there is this Big Exley, The first factor along the tick the narrative line It&#x27;s like I&#x27;m just is equal to you two x and then the constant zeros out. So now we have. But why? Plus X Y is equal to two x divided by co sign of explain And then we can subtract Why on both sides So we have ex wife Frank is equal to two overcoat, a sign of excellent minus way. And then we can divide by X on both sides of the equation to get over co sign of excellent minus y over X or

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.

Ernest Castorena · Answer

the curve defined by this equation are they want us to find the second derivative. So by general, we&#x27;ll have you to the input in time. That&#x27;s the root of the input product Girl will get. Why, uh, sex Weinbrant. Now we&#x27;ll get to I am prime minus three is equal to co sign of Why I product are general. I only want to collect all our wife prime terms on one side. No more will have exceeded the explain Waas to mine is Coastline of White. All of that times Vibram is equal to three minus y times e to the X Y and mountain. We can consult for a while, Bryant used, but let&#x27;s divide now. If it&#x27;s problem, we&#x27;ll divide on both sides by mm, Where was I? That&#x27;s not a viral size yet, because it&#x27;s easier to take the second derivative here. We&#x27;ll get along but the product so we&#x27;ll have that coefficient exceeded. The X Y was to my let&#x27;s go sign away, left untouched because we&#x27;re going to take derivative with second factor, which becomes why prime time. But now we leave that why prime second factor alone and we&#x27;re going to take the derivative of the first factor. So we&#x27;ll get let&#x27;s see General X on a predictable se X turns the one so we&#x27;ll have either the X y and then plus this time the excellent and then do through exceeded the X y. But by Chainarong we&#x27;re gonna have spirit of the input and that needs a product roll. So why, plus x y prime? Get so that&#x27;s the derivative of his first term. Over here, the constant will go away and we&#x27;ll have a plus sign of what times I cramp for negative coastline of wise derivative. No, it looks good on Let&#x27;s take the room on the right hand side. Well, the three is a constant. It goes away and then we&#x27;ll need the product will get Lifetime believe the Syrian Tamerlan and this time will you the first factor alone. So we&#x27;ll have plus negative white times that really with the second factor. But we&#x27;ve taken that one many times already, and we already know it&#x27;s gonna be e to the X wing plus X e to the excellent times that area of the inside, which is why plus X my prime again. And now we can start solving for Let&#x27;s see what&#x27;s to Minus Coast in a way. Seven for a double room. So while on the side we have negative, vibrant times e to the X Y minus Why times e to the X Y plus exceed to the Exline times y plus x y prime. We can divide this after in front of wide Rambam to get that&#x27;s the X e to the X y plus two minus co sign a white I get so I double rhyme Derivative is equals all of this. Well, it&#x27;s almost in terms of just X might if you wanted to, you could solve for why here we all had almost finished that. So we can divide this by ex me to the ex wife plus two minus coastline a white, and that will be the value of our UAE prime. And if you wanted to simplify it, even prove it, you could take this. You could plug it in everywhere you see a white frame, and it would just be in terms of X and y of that school

Problem

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

Problem 5 Easy Difficulty

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

Answer

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Catherine R.

Anna Marie V.

Heather Z.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

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Basic Technical Mathematics with Calculus

Catherine R.

Anna Marie V.

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Precalculus Review - Intro

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

Catherine R.

Anna Marie V.

Heather Z.

Kristen K.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus