differentiate-the-function-hnr-nleft1-fracnkright

Question

Differentiate the function.
$h(N)=r N\left(1-\frac{N}{K}\right)$

Clarissa Noh · Accepted Answer

Hi. This is Claire cell when number 20 26 of Stuart&#x27;s by calculus book. So we&#x27;re going to differentiate this equation. So first we&#x27;re gonna use the distributive property on we&#x27;re going to distribute the equation. So we get are and Linus and square que times are and we&#x27;re gonna different Schapelle signs terms of capital And do you separate? Thes needs someone Fast steel were d capital looks and square We&#x27;re okay, Times are and then we pull up. Constance woodstee over. Be Colin. Couple in Linus, arm over K D. Over. Do you know capital and Square? And when we simplify this, we get our minus tube are tons Kapil on over K, then box it murder.

Clarissa Noh · Answer

he had squares The When you read here, so we have k of our is equal to you are plus r to the power we differentiate We got d over t r each the r plus D over d r Aren&#x27;t the e This just becomes eat the r and we&#x27;re gonna apply the power role for here, and it becomes eats the r plus E times R to the e to the T minus one.

Linh Vu · Answer

even if she thanks in culture, you Teoh I A x plus and therapy and religion Palocci primary function there noticed that we have a power first and we need your bring up our down. Therefore, we have been called you too are a r x plus and Thames be now this spelling bee p minus one and by the general in its attempts that you are a express and the relative. Then we get the culture nous and about being minus one. Now the real deal This one here the river there the any coach Izzo for usually have neighbors That you are is a constant You lived in the, uh, exponential will be staying the same in Thames and an under, uh I Thames. Uh, thanks. The river Dio when there are actually area of the culture, are so we have removed is on a date with a square here and this will be the answer

Clarissa Noh · Answer

it&#x27;s clear. So when you married here. So we&#x27;re gonna take the derivative in terms of our since it&#x27;s each of our for a e to the are over eat the R plus B Then we take that ate out get G over d r Were each the r over eat the R plus B. This is equal to t over de arm or eat the R terms Beats the art plus B minus. Beat the art d over d. R. You two are plus B over eat the R plus B square. Then we put a at the end and when we simplify, you get a times eat are come meet our plus B minus eat Our plus zero kind eats the R all over each the r plus B square. When we simplify yet eh be beat to the r Over eat the R plus B square

Linh Vu · Answer

it was given the function G r equals R square times. And then I&#x27;m that you on this one here? Well, it wasn&#x27;t asking. Defendant she r g parameter are. And here we noticed that we have that you function you envy and religion. Find a project for here You print three plus new fea brim. If I wish to get a culture a square friend attempt and then in that you on this one Then just the our clan comes telling them that you are one you would do. He had lived in the ask when you could do that. You are camps and then of it on this one square temps that the reason the anaemic over the two off this one time over the two are but one and the finest them. We will have, uh, you on this one that they lived in Medina in numerator here. But you chew there found we have pressed. You are square over Geo best one

Nicholas Barvinok · Answer

we want to find the derivative of the function one over s plus que e to the s. And to clarify Kay is a constant and esses are variable So we want to take the derivative with respect to s. So the first thing I&#x27;m gonna do is I&#x27;m going to rewrite this. Just rewrite the function as s plus que e to the S to the minus one. So I&#x27;m doing this because I don&#x27;t want to be tempted to use the quotient rule if I don&#x27;t have to. Because the quotient rule is one of the more complicated rules to utilize when taking derivatives. Whereas if I just have something raised to the power of minus one, the power rule is much simpler. So by the chain rule, I I want to first take the derivative of the outside function which is some function being raised the power of minus one. So by the power rule, I bring down the minus one. Multiply by my function my inter function and subtract one from the exponents get minus two and now, by the chain rule, I&#x27;m multiplied by the derivative of the inter function. The inter function is a sum of two terms. Differentiation is linear, which means that I can take the derivative of each term separately and add those up. So the derivative of s is one plus well again, because differentiation is linear the second. That thing that that means is that the derivative of a constant times of function is that constant times the derivative of the function. So, in other words, I can leave this constant K and just multiplied by the derivative off dysfunction E to the S. And the Dorota of each of the S is just t to the s and we&#x27;re done.

Problem

Differentiate the function. $f(x)=k(a-x)(b-x)$

Problem 26 Easy Difficulty

Differentiate the function.
$h(N)=r N\left(1-\frac{N}{K}\right)$

Answer

$h^{\prime}(N)=r-\frac{2 r N}{K}$

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James Stewart

Biocalculus Calculus for the Life Sciences

Anna Marie V.

Heather Z.

Caleb E.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

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$h^{\prime}(N)=r-\frac{2 r N}{K}$

Biocalculus Calculus for the Life Sciences

Anna Marie V.

Heather Z.

Caleb E.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

James StewartBiocalculus Calculus for the Life Sciences

Anna Marie V.

Heather Z.

Caleb E.

Kristen K.

James Stewart

Biocalculus Calculus for the Life Sciences