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Numerade Educator

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Problem 54 Hard Difficulty

Find $ \frac {d^9}{dx^9}(x^8 \ln x). $

Answer

$f^{(9)}(x)=\frac{8 !}{x}$

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Video Transcript

in this trouble. Where s defines night ordered a veritable eight times. Next level effects. Let's start from for Syria but said that this is our function. This is a PR person fits it and b f p x b eight times x to the seven day trip logo face waas Actually a Do I act so basically I had some sort of thought that is basically just a porter. Cruel. Second, order them to these kurta where he in spirit be eight times seven times extra to six make sure love x waas eight times and shit. It's heaven for over X plus seven six to six And here additional can slug who will have exited sex And we can write this one of the eight times seven times Exodus six nation long affects waas um 15 times X to the sir. All right, now, third order to deejay at Woody It's Jude would then be eight times seven times six times. Thanks to make sure water x waas we have 15. Um okay. We have eight times seven times exited six times one over x plus 15 times six times Excellent. And we can write. This one is eight times, seven times six times extra bit natural x was some constant. So let's just set out that it's C times extra. The the idea is that you see, uh, when was second order never to be had extra six year study. If we had those two are was eight when it disturbs order derivatives, we have five here. So again with me and those are B and not with x six term actually a thermos Or can I just say that we're now interested in e 8 800? Everything off dysfunction, uh, this term would not be able to keep up on we would end up with a constant. So we would have eight times seven times, six times, five times that. That one nation look affects waas uh, a constant. Let's just say you would have constant That constant is this term. All right, now let's take, uh, there was one more time and let's say that we are looking now at Brian's, ordered a rigid and that is what we are you president. Actually, that would be eight times seven times six times all those terms, which would be a factorial now. David tipped off nature Walk off exit. Oh, no, Rex. Plus, there were two of the constant is zero. So from here, we can then say that man colder. There were 59 off sister F D x nine. He's a good to eight factorial divided by rights.