solve-the-given-problems-find-the-general-form-of-the-function-whose-second-derivative-is-sqrtx

Question

Solve the given problems.
Find the general form of the function whose second derivative is $\sqrt{x}$.

Smita Praharaj · Accepted Answer

in this problem, we are asked to find the derivative of the function. Why equals negative to over Cube? Root off. It&#x27;s. We can write this as negative to over X rays to the one third. It simplifies to negative two X rays to the negative one thirds. Now we&#x27;re going to use the power rule to find the derivative off dysfunction. The power rule states that ddx off X rays to the end is going to be end times X rays to than Manus one where n is any number. So now D y over the ex is equals to d over t X off negative to X rays to the negative one third. Now this negative too is a constant, so we can pull that out of the derivative. So that equals negative two times D d x off x rays to the negative one third. Now using the power rule, the derivative becomes negative one third times X rays to the negative one third minus one now negative times negative is a positive two times one third become scooter ds X rays to the negative one third minus one. So that&#x27;s negative. Four over three. So that&#x27;s the derivative off the function

Amy Jiang · Answer

okay, So drastic to us, driven with fallen. So it&#x27;s not really changing our radical into a power that&#x27;s just X to the power of one of the three. And now I&#x27;ll rewrite this as a negative exponents that it&#x27;s gonna go to extra bag. Native won over three, and now I can use our powerful to take the derivative or to get the derivative. That&#x27;s negative. 1/3 times. Think of two accident later, one of three minus one. So that&#x27;s to over three X to the power of one is 3/3, So that&#x27;s negative for over three, so we get the fallen.

Linh Vu · Answer

even the question Sister the white up of Bram. It was Ego Judah Square, bit of the X and in discussion, where he called them the integral expound. The banks were coaching the expert and risk went over and was one. There&#x27;s a constancy and we just question here we can get the white Bram first by doing the integral I&#x27;m the wind of a gram The x don&#x27;t get any cogent interval under for the square root we can read is urging about have the eggs and by formula here get the X power when her dress going on the one plus one plus just want here So I will press a constancy one here and they were getting go to the expert to interact you a very big three intends to press a C one So this will be in a wide brim and with the expression from the UAE Prime weaken Ghenda Why again we do the integral one more time under 203 Next Eritrean tipped you Then press a constant C one Dear the X on now there we can distribute into ju it a term the constant can bring outside Thanks integral to see won t next. And then we should get for this one together. Jill, over three times. Now we bless one to the power of gonna find out of you your money back five attempts to you and then bless seeing one. Thanks. Press and out to sea Jew. So it was fine getting caught for everything. Thinks about my mom. Would you? Plus Say we&#x27;ll expect to see you and this will be the answer for the wife.

Shumayal N · Answer

So for this function, they&#x27;re going to start with the derivative of the outer part and then work our way in to the first thing you see is the square root sign. That&#x27;s the outermost part. So we&#x27;ll take the derivative of that which will give us half. And then you read the inner part as it is power minus. And now you take the derivative of the inter function. So the derivative of eggs is one plus. Now take the derivative of square root of X, which is huh x to the power line. A staff and the derivative of X is one, so we don&#x27;t need to write that on Did you can just rewrite this down so we can take 1/2 square root X plus the square root of X none supplied with one plus one over two screwed of X

Ernest Castorena · Answer

Vega was the function Apple X is equal to the square root of X over X squared plus one. Well, lets him take their a tive on the to do 1/2 of the input. So enough times X x crib plus one and then document the power. It&#x27;s not a negative one. But now when you take that area of the inside and this will require a question room the ruler of the top times the bottom so x squared plus one and minus this time leave the top alone times the derivative of the bomb, We&#x27;ll end up with two X. Does that look right? Mm. Yeah, they&#x27;re the bottom is two X and not all over the bottom square. Well, this is minus two X squared, so end up with a one minus x squared on the number, and that isn&#x27;t I hate cancels with anything in the bottom so we could leave our and say like this. Um, it looks good.

Problem

Solve the given problems. Find the general form o…

Problem 51 Easy Difficulty

Solve the given problems.
Find the general form of the function whose second derivative is $\sqrt{x}$.

Answer

$\frac{4}{15} x^{5 / 2}+C_{1} x+C_{2}$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Catherine R.

Anna Marie V.

Kristen K.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

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$\frac{4}{15} x^{5 / 2}+C_{1} x+C_{2}$

Basic Technical Mathematics with Calculus

Catherine R.

Anna Marie V.

Kristen K.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Catherine R.

Anna Marie V.

Kristen K.

Samuel H.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus