Question
2 2r3 Differentiate_ 87 Vz the answer with positive exponents and radical form_
2 2r3 Differentiate_ 87 Vz the answer with positive exponents and radical form_
Answers
In Problems $87-100,$ expressions that occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. $$ \frac{\sqrt{x^{2}+1}-x \cdot \frac{2 x}{2 \sqrt{x^{2}+1}}}{x^{2}+1} $$
We're given the cue group with eight x plus one food for three times the Q group of X minus two squared. Then that's added to the cube. Grew the X minus two over 24 times the two groups eight x plus one square. All right, in there. Now that we've written down, we're first going. Teoh, See what you can get to get a common denominator so you can add They used to expressions together. So what we're gonna do first is take our three Queudrue it exports one over three. Q group of X minus two squared. We're gonna multiply numerator in the denominator, make that little less confusing and user different multiplication sign. We're gonna multiply it by eight times the Queudrue of eight x plus one squared. So the reason that we're doing this it's because when we take this eight right here and multiplied by, this three will get 24 so we can have a common denominator. And the reason that we're doing that eight x plus one squared is against That's also part of, um uh right side expression. No, you'll notice is now with our other side. We're gonna multiply this Sorry. That's Reinold. Play this side over here. Let me rewrite it. First, we're gonna multiply this side by the cuter. The X minus two squared again. The reason that we're doing this, it's so we can have a common denominator because you'll notice that this expression is a miss side. So now when we multiply this out in search to a new all right, we'll scroll down new future there. So now that we've got those, we can multiply them out, which will give us we'll explain this little better. So we've got or 24 with these here. We've got 24 with these here. So now we can just work and do the addition up here. So this is the part that we're looking at. Sorry to those they're not distracting. Scroll down. So know when we add all of these together we've got age. Times eight exports one plus X minus two. That's going to be over our denominator that we have created 24 8 x close fawn to the 2/3 power multiplied by X minus two to the 32 3rd power. And from there well, just multiply it out, which gives us 60 64 eggs plus a plus specs minus two. So I make that a little clear, close, and that's gonna be overcome. Denominator. Once again, 24 it exposed one to third times X minus two to the 2/3. And then from there we can just simplify, which will give us 65 x plus six over 24 times eight x plus one the 2/3 times X minus two 2/3 flower. So this will be you complete.
Okay, So what stepper be writing our exponents as a rifle? So that's the square root of 25. Well, 25 it's five cpac two. We have X squared. And why? So this is equal to five x square root of wine.
In this problem, we have toe solve this value. So using the quiet and rule so using quietened rule which is given by this formula. So I will use this formula to solve the question. So on using this I can write this value as this under root access squired by under Route 49. Now going forward and solving this, I can write it like this x by seven it is requires under root access squared is equal to X and under Route 49 is equal to seven. So the final answer for this question is X by seven. This is our answer.
We'll start with the square root of two on the top and the square root of 49 on the bottom spirit of two is just swear to two and it's quarter to 49. You know it's seven so radical to oversee.