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Question 9 of 22View Policies Current Attempt in ProgressDifferentiate the function f(r) = 7"+9' f()Save for LatedAttempts: Qof 1uscd "t...

Question

Question 9 of 22View Policies Current Attempt in ProgressDifferentiate the function f(r) = 7"+9' f()Save for LatedAttempts: Qof 1uscd "t

Question 9 of 22 View Policies Current Attempt in Progress Differentiate the function f(r) = 7"+9' f() Save for Lated Attempts: Qof 1uscd "t



Answers

$7-18$ Use Part 1 of the Fundamental Theorem of Calculus to find
the derivative of the function.
$$g(s)=\int_{5}^{s}\left(t-t^{2}\right)^{8} d t$$

Function are off white, equal to in trickle. Why? To to tq sign t DT. So in this kitchen, we have to use part first of fundamental theorem of calculus to find the derivative of the function. So you can see that there is a lower limit its why and of our limits to So we have to entertain the limits. So we know that here the property a integral a b f of x d x yeah, equal to and regal apple x d x And here is limit be to a But we have to put the negative sign for interchange the limits. So we apply that property here and we get are of y equal to your negative sign and wriggled. Did you time sign t DT limited to do I We know that. Okay, The fundamental Terram of Part First, which is D in trickle f p DT upon D X equal to f of X. So you can see that here is limited a two eggs. Now we apply that property in this function. So here are function is or of why equal to negative country girl de que time sign d DT and limited to do I So, first of all, we have to differentiate both sides with respect to why? So you can see that here or the video are of why equal to negative d in trouble Take you time sign t d t upon dy so you can see that there is limited to two Why so we partier and we know that equal to we get fr fi So here we have to put equal y So we get y que time sign Why? Which is negative Because here, as you can see, that negative sign So delivery of our of y equal to negative yq time signed Why it is all final answer.

Function g of X equal to into you. Of course, T square, DT 12 X. So in this kitchen, we have to use part first for fundamental Europe of calculus to find the derivative of the function. So here we know that mhm the fundamental theorem of calculus part first we have to use here. So we know that the fundamental theorem of calculus Spot force which is D in triangle fft DT upon p X here 82 x equal to a full facts. So here we use that term and we have to differentiate g of X to the both sides with respect to X. Then we get derivative of cheap X equal to B and Regal. Of course, the Squire DT 12 eggs upon D x. Okay, now here you can see that to the Tehran we get f of X. So here we're plugging equal to x. So here, report X then we get calls. Mm x is quiet so we can say the everybody of G of X equal to, of course, X squared. It is all final answer

Edge of X equal to been triggered Signed to the powerful the DT two one upon X. So I left u equal to one of one a. So do you upon the X equal to negative one upon x square So now we put x u equal to one upon X So here we get and we differentiate it So here we get derivative of G Oh, sorry. Edge of X equal to B Incredible Saying fall to the power D DT do do you upon dx So here we apply chain rule and we get the incredible sign to the power for t d t due to you upon do you game the you upon DX. After applying channel we get this and to the fundamental thorough we get signed to the power for you time We know that the value of do you upon d x equal to negative one upon x square. So we put here and you equal to one upon X. So we put here and we get signed to the powerful one upon x negative one of them like square. So now you can write the review of edge of X equal to now you do? One of on exit Squire. Sign to the powerful. Going up on X So it is over. Final answer.

Here we have a chav X is equal to the integral from one to eat of the X natural log of T d T. And we're going to go ahead and evaluate the derivative. Excuse me. We're going to find the derivative. Um, let's find the derivative using the fundamental theorem calculus that's we're gonna dio. So the derivative is the integration and evaluated at each of the X, and then we're gonna multiply by the derivative of E to the X So natural log of E to the X is just X and the derivative of E to the X is e to the X.


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