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Point) Find a formula for f-l(x) if f(x) = X +)' f-1e (x)(f-1) (x)...

Question

Point) Find a formula for f-l(x) if f(x) = X +)' f-1e (x)(f-1) (x)

point) Find a formula for f-l(x) if f(x) = X +)' f-1e (x) (f-1) (x)



Answers

Find a formula for $f^{-1}(x)$ $$ f(x)=3 / x^{2}, \quad x<0 $$

So this is kind of a continuation of problem number four eso in number four. We actually find that partial derivative with respect to X is this And what perspective? Why is that so? I won't go over that again. Um, but if you do want to go watch, I would just go back earlier to the chapter and watch that video on how we got that. But just in case you've already seen that we don't need Thio go through this again because now we can just plug these values in. Um so let me get rid of these a rose and scoop this down a bit. So first, we're gonna have f sub x of negative 12 servers gonna plug in X and y eso This would be four times negative one and then two squared, which is four all over Eso it just be one plus four squared. And then the new mayor, that would give us negative 16 over. So five squared. So 25 so are partial derivative with respect to X at the point, negative 12 is going to be negative. 16 over 25 and then for us to find our partial at this point or why? Same thing. Just plug in the points. So b f Y r f supply at negative 12 So we're gonna have negative, or and then we'll negative one squares. That's just one. And then, wise be times too all over. Well, actually, I forgot to square this, Um, so then we plug those in, so gonna be one plus four all squared. So that would give us negative 8/25. So that that is our personal with respect. Why? At negative two. So again, if you haven't seen number four or you haven't gone through number four yet, I would go back and watch that video so you can see how we arrived at thes partial derivatives here. Um, and then you could come back, and at that point, it's just lugging the values. It

Okay, so what? You been up back? And we want to find after Prime Obey. So it's step by finding everyday so that you could create a directory. So let's put that into our following equation here. So we have exited her three minus eighth, your heart brain all over X minus a. So in our new murder, we have a difference of two cubes. So it's factored up into X minus aim times X squared plus a X and in plus a squared all over X minus a. Now we can cancel out our like tens and I Let's use deck sub. So here we have a squared plus eight times a plus a squared. So this is equal to three a squared.

Okay, so we're giving our fallen function and we want to find f Prime Obey. So it's no, um, in our equation. We have other blacks that's given, but we need to find every day. So every day that's acquitted. Three a minus one. So now let's put this into our equation. So that's the limit. As except for just a of three X minus one minus three a minus 12 X minus three Aim plus one Looking counsel outs are like terms, and this is all over X minus fame. So it's builds that inner numerator. We have a, um, three in common, so it's back it out, and then we have X minus aim over X minus a. Let's cancel out, or like times when we see that here are limit value. Is he good to three

In this question we have to differentiate the function that is. I can say that At x equals two Axis Square into three x cubed -1. Okay, so differentiated. We are going to apply here. Products and I'm going to stay the product. The product rule says that if you have the product of FMD function and you have to differentiate then you can say that first as it is and the relative of second means a jew dash G as it is and the relative of first. Mainzer dash. Okay, so we have to apply this product so we can say that after applying this product we get the derivative that is after taxes, it was to access whereas it is and the negative three x cubed -1 plus three X cubed minus one as it is and derivative access work. Okay, so I had written the Julia. Now I'm going to the french here here. So it's a swearing to that. You do three excuses. nine at 6. zero plus three xQ minus one. The reality of process where it's two words, okay, now we make the product here. So we got nine express to de power food plus six x rays to the power four and minus often works. Okay, now we add nine and six. So we get here 15 access to the about 4 -2 works. So this is the value of derivatives that we go out here. Now in this portion, it was told that we have to find the creative At the point that is 1:02 years. So I'm going to find 500 derivative at the point that is one former to means I'm going to put here at the place of X one and it's a 15 1 here. We got to turn into one of the about 4 -2 into one And their changes into I can say that 15 -2 minutes 30. So what do you need the final answer of this question here? Okay, thank


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