find-the-derivative-of-the-function-fxx2x

Question

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

Ernest Castorena · Accepted 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

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

function F of X is equal TV X over tilea. But here in this recognize this is just e over to to the expiring together. Now let me take the route If we can just take the natural log of the base some natural large of hell where to times same excellent function. And while let&#x27;s explore that coefficient a bit more, we have the natural log of et minus. The natural log on to times are original function. The older to you natural law gov is just one. So what we actually have is one minus. The natural log to times are original function he over to to the axe part awesome.

Rakesh Kumar Sharma · Answer

the question we have off, friend are consistent for fortune exit Excuse to There you go X squared minus one day We&#x27;re going excess worthless. Thanks for more than first the function Fact rages when reading. Explain this one Do express one. I think that you know I love you need X, you know, express mail. So that begins ing out before this is defined. So he warned me about the radiators Extender X into selecting nexus where okay and us Mr. Election didn&#x27;t. And this week, extended by this one&#x27;s the cool expires actually getting less sex and my miss food derided by yes, and for those of X Let&#x27;s run My Mr by accident is off. What flex differently of dysfunction. Many gadgets, by little signifying formation, hold different station. And that&#x27;s a very good technique. So officiated knows their differences Different station Actually, when we used to go and the physician off minus two y esquire minus to buy extra a week less through by excess fire. So that is that

Ernest Castorena · 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.

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.

Problem

Find the derivative of the function. $$f(x)=x 4^{…

Problem 3 Medium Difficulty

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

Answer

$$1+2^{x} \ln 2$$

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Robert T. Smith, Roland B. Minton

Calculus: Early Transcendental Functions

Catherine R.

Kayleah T.

Kristen K.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

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$$1+2^{x} \ln 2$$

Calculus: Early Transcendental Functions

Catherine R.

Kayleah T.

Kristen K.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Catherine R.

Kayleah T.

Kristen K.

Samuel H.

Robert T. Smith, Roland B. Minton

Calculus: Early Transcendental Functions