Dibeaertiaia3-24 ()f6)#2(1) fo)#rerf(x) = tanx 4sin *(4) f(x) = Vx+ 1...

In Exercises $43-62,$ find the derivative of the function.
$$
y=8 \arcsin \frac{x}{4}-\frac{x \sqrt{16-x^{2}}}{2}
$$

In this question. Well, even function why he code you, ah, half times the x times the square, the four minus X square plus four times the Exide off the X over to and want to find a white prime on the function. Yeah, Before we do the white prime, I will remove blanket. Yeah, Then it has such a big times. And then this comes to only And now don't you find a white Bram? This one will give the half outside first. And for this one, we need just like the product rule. So they refer to the exit to one. So when the square root of four minus x square and now plus ex Thames the review on the squares to have the to stem square in the four minus x square they revert to their former X squared equal to the minus two X. And now, for the second term, we bless the two outside we lived in the X I echoed you one divided by square under one Manus X squared over fall and by the general we need two times the an ex opportunity derivatives we have use only be a half year and Now what? You need to simplify this expression here. I'm going to put everything into the same common denominator here. So we have the two times two and 10 squared on the farm and X square, and we have here will be the ah eight minus two X square minus two X square. And for this one, we have two kids and I wanted to And we can bring the for square the fire. Could you choose? So, just to our square, the four minus X square and now all the time we have the aid can be funded by fire or equal to do and then minus x square over square root on the four minus x square, plus two over square with the four minus x square. And then we can end them up together. Square under four months. Next square in the denominator on the time we have four minus x square so we can cancel them together. Square in the four minus x square

Here we have to find the derivative off up, off the ties equal to one upon for signs to care. Do Tita Okay, we can write The human function is went upon for into sign off to theater. Also care now implying the general we have applying the general once we have FDA show off the dial physical toe went upon four is a constant So people outside now bring the exponents first and sub Drake went from exponents We have one times they're ready for off It's best signed to theater So we have one upon for into to sign to theater the rate of off scientist dies Course Tita again applying the channel we have de upon the theater in tow with you Dad So we have went upon for into to sign off to teacher cause to theater into the video for two theta is too now went upon for into two times two is for sign to teacher cause to theater we can cancel for So finally we have sign truth It course to the theater which is the required They're ready for the human puncture

This question. We call about the revenue off the act tension so it will have dungeon on the function of the X derivative. They were getting close to the U prime X over the one plus new square on the X in discussion with even the function Why you got you. Hey, we have the ANC's attempts the ANC dungeon off the two X and now minus 1/4 times the Ireland under one plus four X Square. Now we want to find a white prime the first term here. We need to apply the broader rule here now They lived in the act because you one saw him. The act tension on the two X now plus X times now by formula here the river, the two Xing to do the running by one plus two X square, equitable for X square and then minus 1/4, they leave the island. Here we go to the one plus four X Square on on the top. The review. Under one plus four X Square, they go to the eight x and it was 75. Get ego to no act. Dungeon under two X plus two X divided by one plus for X square. For this one, you can cancel. Listen then we have a Jew left managed to exit invented by one plus four X square. We say we can cancel these two out and then we have left with only the X tension under two x.

In this question were calling up under the ribs to have the inverse chicken magic. So if we have the thank sigh off X derivative, then we should get equal to the one off, uh, square root off the one minus thanks square. And now it would replace this one, bind you off X. And then this one should be that you have x here and then by the general we need your times, do you prime on the X And now in this question, we even the function f x you go to the to time the X sign off the X minus one. And in this case, this one will be the year of the X. And by the formula, we can find the aircraft on the X. We should get equal to the constant stay the same and by the family was gonna one divided by the square root of the one minus the U square citizens stories. You square here don't have the X minus one square and by the general we need your attempts that derivative the X minus one crime here and eventually we get equal to the to because the river the lesson equal to one, so you have to over a square root after one minus X minus one square and this will be the answer.