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Numerade Educator

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Problem 53 Medium Difficulty

Find a formula for $ f^{(n)}(x) $ if $ f(x) = \ln (x - 1). $

Answer

$(-1)^{n-1} \frac{(n-1) !}{(x-1)^{n}}$

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Video Transcript

uh, trouble were given a collection effects as nature love explains what you're arrested, fined and ordered their bitter, uh, dysfunction. All right, Lester quality first. Very quiet moments. Now, knowing that perfect is natural explains when we see that affects it will explain us what we can write this one as X minus one in earth. Now let's look at the second order. Derivatives that double prime of X B negative born times X minus fallen negative too. Now, first order their best people. Probable effects would be negative. One has negative two times x once one too negative. Third forward and F or X 40 Negative on negative too negative. Three comes excellence for pretty negative for power. I think we see the pattern here. So we're trying to find and all ex. Okay, one be ordered off. Decorative is off. As you can see from here, the term get is positive when the order for there to this, even the term we get For the devotee of the sign, both the director is negative. So we can I first not oneness, negative or power and plus fall so that all terms will be positive for negative. Also As you can see when it is the second order, inevitably have negative. All order would give us going to one time. Say headed to court order is for time to Time Street. So we're gonna have a minus form pictorial. And here we have explained this form to the end. Follow. We can right then from this F and 40 Gavito X has negative one Kirsten plus one off. Bye bye. And mind school factorial you wanted by X minus war to the end How?