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Question

Find the derivative of the function.
$F(x)=\left(x^{4}+3 x^{2}-2\right)^{5}$

Amrita Bhasin · Accepted 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

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

Rakesh Kumar Sharma · Answer

and especially ever find out that people X Q minus works aspire this fight in new accessible four minus three Xs fire list Okay, they&#x27;re defined over today using for the cool. So for that first started two days, we&#x27;ve been defensively despite before. So differentiation off excuse will be three Xs where minus I want to do for X And the position of this part of doing so existed before my city excess fired those two first now different. You&#x27;re despondent, he said the sensation and, uh, this party needed me as it is so excessive. R cubed minus two words is where plus five into different vision of this position. Almost 54 excessive RQ minus 66 And that doesn&#x27;t differentiation off. Even fortunate. With this, it&#x27;s

Rakesh Kumar Sharma · Answer

in this issue. I know the most of the people. Deforestation off function affects is you assume Texas. Where where? G us five. By access for the first day, they were defusing. Moaning are who? X, my tea and the precision off. This will be if you could take excess firing. Doing the best that b minus two times. Oh, just about this one in five. Okay, The sensation for this With me who exploit three minus. I execute that position for you.

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.

Romaila Saud · Answer

find innovative off giving function. Why equals three X divided by four x plus. To clarify, you need to identify the marina the inner function. You can be written as three effects, divided by four x plus to the ultra function. Why I can&#x27;t do it and as y equals u to the power off. Five. Do you buy? The X can be evaluated by using Potion Group. That&#x27;s do you buy the extended Britain as DE by the X off three x into four x plus two. Minus deep by D X off four x plus two. Can&#x27;t do three x divided by four x plus two old square. Next we&#x27;re simplifying. To get three into four x plus two minus three x into four divided by four X plus two whole square. The final expression can be evaluated as 12 x plus six minus 12 Lex divided by four X plus two whole square After simplification, do you buy The axe becomes three divided by two into two X plus one whole square. Next we find do you buy? Buy do you B. Why buy? Do you can be written as five into you to the power off for putting in the value off you that you&#x27;ve already assumed de vie by the U becomes five into three x divided by four x plus to pull to the power off. Four. In order to find d y by D. X, we next apply chain grew, which is D Y by D. X equals divide by you into the u by d. X Putting in the values of each of these expressions that we&#x27;ve already evaluated. We get five into three x divided by four x plus two to the power off war into three divided by two two x plus one Hold square. We can get a final answer after simplification, which happens to be 1215 into X to the power four, divided by two into four X cross tube the power off four into two x plus one Hold square

Problem

Find the derivative of the function. .$F(x)=\lef…

Problem 7 Medium Difficulty

Find the derivative of the function.
$F(x)=\left(x^{4}+3 x^{2}-2\right)^{5}$

Answer

$F^{\prime}(x)=\left(20 x^{3}+30 x\right)\left(x^{4}+3 x^{2}-2\right)^{4}$

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James Stewart

Biocalculus Calculus for the Life Sciences

Grace H.

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Precalculus Review - Intro

Functions on the Real Line - Overview

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$F^{\prime}(x)=\left(20 x^{3}+30 x\right)\left(x^{4}+3 x^{2}-2\right)^{4}$

Biocalculus Calculus for the Life Sciences

Grace H.

Catherine R.

Kayleah T.

Caleb E.

Precalculus Review - Intro

Functions on the Real Line - Overview

James StewartBiocalculus Calculus for the Life Sciences

Grace H.

Catherine R.

Kayleah T.

Caleb E.

James Stewart

Biocalculus Calculus for the Life Sciences