calculate-the-derivative-fxx5-44-x-3-211-x

Question

Calculate the derivative.
$$
f(x)=x^{5 / 4}+4 x^{-3 / 2}+11 x
$$

Elyse Gonzalez · Accepted Answer

hi. Today we will be learning how to take that around of off the following the creation Halifax equals X to the power of five over four plus four times X to the power of negative three over two plus eleven x. So first, let&#x27;s do a small review on how to take the Druid. Let&#x27;s say that I want to take the derivative off a function, and DD X is just signifies that you want to take the derivative of something. Let&#x27;s take the derivative of X to the power of any number I the driven of that would just be I Times X to the power off I&#x27;m minus what So say that I want to take the derivative off x squared four. Yeah, that&#x27;s right like that. It would simply be two times X to the power of two minus one, which is just one. No, it&#x27;s opposing. You had a constant in front of the ex, so let&#x27;s say we want to take the did it. The directive of C Times X to the power off any number I see being a constant number, like two or three now because see doesn&#x27;t change with X. We can actually take constant outside of the derivative Vince. They see times the derivative or D T X of X to the power off I. So let&#x27;s say that we want to take the derivative of two times X to the third power, the derivative of that or DD X Off. This function would be two times three off X two, three minus one or X squared, and that&#x27;s equal to six Pecs Square. So now, knowing this, we can solve for the derivative off our function above so we can take this in parts. First, let&#x27;s offer the derivative of X to the power five or four. This would be a prime off X just signifies the derivative FX of Prime Facts equals five over four times X to the five over four minus one five over four minus one is just one forthe soul right like this. Now let&#x27;s take the derivative of four times X to the power of negative three over, too. Now First will multiply four times negative three over two and will get six Now. Keep in mind that because negative three over to his neck, never going to write minus six because for turn negative. Three over to his negative six times X to negative three over two minus one, which is negative. Five. Over to now, let&#x27;s write the derivative off eleven X or eleven times. Act to the power of one. Eleven times one is just eleven x to the power ofthe one minus zero is next to the power. Sorry, excellent. Half one minus one is X to the power of zero. And actually carve zero is just one. So it&#x27;s eleven times one or just eleven. And there you have it. That&#x27;s your derivative for FX. Thank you for watching.

Foster Wisusik · Answer

Okay, so this question wants us to find the derivative. So again, we&#x27;ll just power was his power rule each term. So we just supply the derivative to each of these terms. So we bring the exponents down and decrease the power by one, and we do it again for each term. Be extra careful with your negatives. And remember the derivative of a constant this year. So simplifying we get 23rd X to the 2/3 plus six over x cubed because X to the minus three is just one over execute plus zero. So this is F prime.

Ernest Castorena · Answer

the function of a Rex is equals x to the 10th minus three x to the fourth plus two x minus on. And then they want us to compute the fifth derivative. But know that the fifth derivative rules they were out any polynomial. Let&#x27;s degree for less so we won&#x27;t care about the rest. Take our derivatives. Let&#x27;s see, the first derivative will give us 10 x to the ninth will be some stuff over. Alright, second derivative. Well, give us but seeing 90 x today. Some of us over right there, derivative. Well, give us seeing 90 times eight next to you seven means I&#x27;m not covered. And Lynsey, our fourth derivative Willie, was my district time. Sometimes nothing. Be time. Seven Thanks to the six one term leftover Probably lineup. Now 50. It&#x27;s the only time left over. Well, in the book. 10 times nine times 8 10 76 X to the fifth and the rest of the terms. Evans, Right out. So this is our derivative doesn&#x27;t

Amrita Bhasin · Answer

this question gives us off our backs is ext the fourth plus three X squared Rennes Toots the Power five and asked us to find the derivative. What we know is that for the first part, we can take the exponents and make it our new coefficient. What&#x27;s inside stays the same and then we can decrease the experiment by one to make it for now. Next part. Let&#x27;s use the chain rule, Which means let&#x27;s take the derivative of the inside. The derivative of X to the fourth is for X cubed, the derivative of three X squared is sex sex and then lost Lee. It&#x27;s usually good form to simplify. We can simplify this to be 20 acts cubed plus 30 acts Times X the fourth plus three X squared minus two to the power for

Foster Wisusik · Answer

Okay, so we&#x27;re asked to find the derivative of this function. So to do this, we use the power rule on each term because the derivative is linear. So it&#x27;s the derivative of two x cubed, plus the derivative of negative three X squared, plus the derivative of five. And for the first term, you bring the three out front times two x lower the power by one plus I can bring down two, decrease the power by one and then the derivative of constant zero. And then if we simplify, these multiplication is going on. Here we get six X squared minus six eggs for our F prime.

Heather Zimmers · Answer

Let&#x27;s find the derivative of F of X and F of X is a product. The first factor is two X minus three to the fourth on. The second factor is X squared plus X plus one to the fifth. So we&#x27;re going to use the product rule. So we start with the 1st 2 X minus three to the fourth times, the derivative of the second and the second is a composite. So we&#x27;re going to need to use the chain rule. So the derivative of the outside the outside would be the fifth power function, So we would bring down the five and raise the inside to the fourth. So that takes care of the derivative of the outside. Now we multiply it by the derivative of the inside, the derivative of X squared plus X plus one would be to X plus one. So what we&#x27;ve done so far is the first times the derivative of the second. Now we&#x27;re gonna do plus the second X squared plus X plus one to the fifth times. The derivative of the first and the first is also a composite. So we&#x27;re going to use the chain rule to find the derivative of two X minus three to the fourth. The outside function is the fourth power function. So we bring down the four and we raised two X minus three to the third. And now we multiply by the derivative of the inside. The derivative of two X minus three is two. Okay, so we have our derivative, and now it&#x27;s a matter of simplifying. So this entire first part is our first term. And this entire second part is our second term. Squeeze my one back in there. Let&#x27;s see if we have any common factors that weaken factor out of both terms. It looks like both terms have two X minus three. This one has it to the fourth. This one has it to the third so we can factor out two X minus three to the third from both of them. And it looks like both terms have X squared plus X plus one. This one has it to the fourth. This one has it to the fifth so we can factor out X squared plus X plus one to the fourth from both of them. So then the remaining factor, what we still have in the first part. We still have a two X minus three. We still have a five and we to still have a two X plus one. So we&#x27;ll put the five first five times two x minus three times two x plus one plus. Now let&#x27;s look at what we have left in the second factor the second term. So we factored out four of these and we still have one left. So we still have X squared plus X plus one. We still have the four. We still have the two, and we factored all of those. So four times, too. We have eight times X squared plus X plus one. Now it may not be important or necessary for you to do all of this simplifying. It just depends on what your instructor requires, but it&#x27;s good to know how, just in case you need to. Okay, the last thing I&#x27;m going to do is simplify this and I&#x27;m going to do that by using the foil method on the binomial, distributing the five and then combining like terms distributing the eight as well in combining like terms. So we&#x27;re going to have are two x minus three cubed our X squared plus X plus one to the fourth. And then okay, when we foil, we get four x squared and we&#x27;re multiplying that by five. So 20 x squared we get plus two x and minus six x So that&#x27;s minus four X. And we&#x27;re multiplying that by five. So minus 20 x and we get minus three and we&#x27;re multiplying that by five. So minus 15 we distribute the eight we get eight x squared eight x and eight. Okay, the last thing we need to do is combine the like terms. Gonna give ourselves a little bit more room to work here. And here&#x27;s what we just had on the last step. So we&#x27;re going to combine 20 x squared and eight x squared, and we have 28 x squared. We&#x27;re going to combine negative 20 x and positive. Eight x. We get negative 12 x and we have negative 15 and positive eight. So that would be minus seven. So that times the other factors gives us are derivative in a simplified form

Problem

Calculate the derivative. $$ g(z)=7 z^{-5 / 14}…

Problem 24 Easy Difficulty

Calculate the derivative.
$$
f(x)=x^{5 / 4}+4 x^{-3 / 2}+11 x
$$

Answer

$\frac{5}{4} x^{1 / 4}-\frac{6}{x^{5 / 2}}+11$

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Jon Rogawski & Ray Cannon

Calculus for AP

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Anna Marie V.

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Precalculus Review - Intro

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$\frac{5}{4} x^{1 / 4}-\frac{6}{x^{5 / 2}}+11$

Calculus for AP

Grace H.

Anna Marie V.

Kayleah T.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

Jon Rogawski & Ray CannonCalculus for AP

Grace H.

Anna Marie V.

Kayleah T.

Kristen K.

Jon Rogawski & Ray Cannon

Calculus for AP