find-the-derivative-of-the-function-fx1-21-x

Question

Find the derivative of the function.
$$f(x)=(1 / 2)^{1-x}$$

Ernest Castorena · Accepted Answer

It was the function of Lex&#x27;s legal team and C 1/2 to the one minus expert Well, in C, we can take the derivative of this. We&#x27;ll just have natural logs of 1/2 assed we&#x27;ve seen important last year. That&#x27;s two to the negative one natural so we can take that negative one out in front. So we get natural. Love it too. So it&#x27;s natural log of the base. Then we need Teoh. Multiply it by that very same 1/2. So the one minus six part and now chain wrong. There is a negative X over there, so by by a negative one. So we see that our negatives cancel out and we just end up What natural log on to times 1/2 1 minus X awesome.

Ernest Castorena · Answer

we can get expert on the sudden. Absolutely. Let&#x27;s do the rivers. Let&#x27;s get coat, engine and rest of acts on this side. And let&#x27;s get expert over white because we&#x27;re gonna find our derivative use an implicit differentiation. We&#x27;re going to take coat engine of both sides. So we ended with X on this site and co attended of X squared Over. Why here And now we can take the derivative district taxable sides of the equation and we get one is equal. Teoh Co Sikkim squared. That might be negative. Coast begins word, actually. That me and double check. Really quick. Seen my table of it. And it is I&#x27;m looking for the content. Didn&#x27;t, huh? It was that negative coast. He conspired. Okay, No, that&#x27;s going to be of the input X squared over way. And now we need to take the derivative of the input. But we can do product role for that. An expert and the one over white home. So we get two x leave the violent are one over while. And now leave the X squared alone and take the derivative of the one over white him. Let&#x27;s see. No, no. Uh, we need todo chain RL actually still will have an additional when we took the derivative of one over white. Why isn&#x27;t unknown function of X so we also need an additional general. Why prime? There we go. And now we can solve. So let&#x27;s see. Cosi can is just over sign so we&#x27;ll have negative science word. Ah, X squared, overweight. Um, I see. On the right hand side of the equation will have two X That was one of your way minus X squared over Y squared, my friend, So we can solve for y prime by getting this all over to the other side. So we&#x27;ll have negative two x over y my science word over squared over wine. And then that&#x27;s equal to negative X squared over White Square. But we can want supplied by the reciprocal of that. So these negative signs will cancel out Bye bye, y squared over. Explain. All right, so that&#x27;s our revenue. But if you want to get rid of the same square in terms we could direct science period of some form, uh, co Italian coast again again, and then find the relationship with code 100 and you plug in the UAE as well. But this is a perfectly acceptable version of the derivative. As long as you know the point. Do you want to take the road of at

Ernest Castorena · Answer

they function after Lex&#x27;s plus two to the X. Well, how do we take the derivative of a base to the X? Let&#x27;s see if we could write this as he to the natural log of X with be in front of him. Okay, Let&#x27;s see now. That&#x27;s not right. We want to write it into the cool inform either the natural log. And I must break that up because we&#x27;ll have Peter the X here, then. Probably. Uh huh. My rule with longer them so you can take this part to the front. So it&#x27;s the product of X times natural log of me. So this function is actually equivalent to this. And if you wanted to take the derivative of either side I&#x27;ve seen through this is gonna be equal. Teoh, let&#x27;s see. Get anything is just either that anything times the China So we have natural law could be in front. And let&#x27;s see, we can rearrange that. Put this except here. And then each of the Allen cancel out. So we end up with natural Lockerbie. Time was beating the X. So that&#x27;s a refresher. On what? These derivatives. I had to get him. So let&#x27;s take a derivative of a function term. By term, you just get one for the Ekstrom. And here, as we just saw, we got natural log of the base. The natural love too. Times that same function to the X.

Ernest Castorena · Answer

problem they give us of elects is equal to X squared minus one squared all over X squared plus one. And when we take our river, the blood scene we hate the rid of the top first. So it&#x27;s Chainarong. Well, uh, to times X squared minus one times drinks. And then let&#x27;s see, uh, I won&#x27;t supply by the bottom so we&#x27;ll have an X squared plus one. And then for another term, we&#x27;re gonna need to minus, Let&#x27;s see. I don&#x27;t know. I try to move this over its here about So we&#x27;re gonna track this time taking the derivative of the bottom, which is just two X and most of finding by the top, which is an X squared minus one squared, then all over X squared, plus one to the fourth power. It&#x27;s worried. So let&#x27;s see if we can simplify the numerator a little bit. We can factor out and x squared plus one, maybe even two x. So it&#x27;s plowed two x that an X squared minus one term. So an appointment to see you pulled out the two X and the X squared minus one. So we just have two x squared plus two. And we did a similar thing here. And we only have one more X squared minus one time here, the minus X squared plus one. And this would turn into an X squared. Let&#x27;s see if this was a plus two. And this is a Munsey with science clips my sex squared than Usman me and a boy with X squared plus three. Okay, that looks good. So ended with two x times X squared, minus one times X squared plus three all over X squared plus one squirt. Okay, awesome.

Rakesh Kumar Sharma · Answer

It is a question if I know that dispensation for therefore fixes assume works, doing it right, except for this one. Okay, so the differentiation of me, that&#x27;s their definition of the new position. You think? Do you know about this? My differentiation of the development. So that would be flex do anyway, sweat off. You know more of his father&#x27;s indifference toward beauty. For Texas. Where? What&#x27;s to free? Who is this? Where must to minus four x Aspire. You are right next to this one. I just find it who minus no excess where I just like this one. So that is a politician.

Philip Christensen · Answer

to. So for the derivative of y equals two to the ex all over. To do the X plus one need to remember the one rule of power functions Rex exponential functions for any exponential function of a constant pay to the race of the X power. The derivative of that is a to the X power times the natural log A now going back to why we need to use the quotient rule here so well, I prime equals to to the X plus one times the derivative of the top so to to the x natural log with two. Now I can safely move that away and then So we done do minus the derivative bottom. So that is also to to the X natural log of to times to to the x she raised my ex. This is all divided by to to the X plus one quantity squared. Now we can expand this and simplify a bits because get so to to the X times two to the X is equal to the exponents added together. So we can x distribute on the top on the left side of this its attraction get to to the two acts natural log of to plus to to the X natural order to Dan things out of the way. Now I&#x27;ll just erase it Now begins Fracked Distributing the to in the act So I get to to the to axe after a long to we can quickly see here that the to the ex natural twos will cancel for two to the two X So we are just left with and then we have to remember this is all divided by to to the X plus one squared. So we continue this and simplify. So we get to to the X natural law to divided by to to the X plus one quantity squared that see derivative why space?

Problem

Find the derivative of the function. $$f(x)=\frac…

Problem 10 Easy Difficulty

Find the derivative of the function.
$$f(x)=(1 / 2)^{1-x}$$

Answer

$\left(\frac{1}{2}\right)^{1-x} \ln 2$

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Robert T. Smith, Roland B. Minton

Calculus: Early Transcendental Functions

Catherine R.

Anna Marie V.

Caleb E.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

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$\left(\frac{1}{2}\right)^{1-x} \ln 2$

Calculus: Early Transcendental Functions

Catherine R.

Anna Marie V.

Caleb E.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

Robert T. Smith, Roland B. MintonCalculus: Early Transcendental Functions

Catherine R.

Anna Marie V.

Caleb E.

Samuel H.

Robert T. Smith, Roland B. Minton

Calculus: Early Transcendental Functions