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 May 16th, 2017, 08:45 AM #1 Newbie   Joined: Jan 2017 From: brussels Posts: 28 Thanks: 0 Differentiation At any time t seconds the distance (s) metres of a particle moving in a straight line is given by s = 4t + ln (1-t) Express an equation for the first differential then rewrite as a function of a function, now determine an equation for acceleration d^2s / dt^2 and its value after 1.5 seconds May 16th, 2017, 09:04 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 If you are asked to do a problem like this, asking you to find the first and second derivatives, you must be taking a Calculus class. Surely, you have learned how to differentiate, haven't you? The derivative of 4t + ln (1-t) is the derivative of 4t plus the derivative of ln(1- t). I would expect you to know the derivative of 4t. To find the derivative of ln(1- t), use the chain rule. Let u= 1- t so that ln(1- t)= ln(u). Then d(ln(1- x))/dx= (d(ln(u))/du)(du/dx). Do you know the derivative of ln(u) with respect to u? Do you know the derivative of u= 1- x with respect to x? Thanks from topsquark May 16th, 2017, 12:17 PM #3 Newbie   Joined: Jan 2017 From: brussels Posts: 28 Thanks: 0 Yes I am, but I missed a large part of the calculus unit due to illness, so now I'm looking for a bit of guidance. I think the part I struggle with most is understanding the equations and what it's asking for. Thanks for your help. Last edited by skipjack; February 8th, 2019 at 03:15 AM. May 16th, 2017, 12:59 PM #4 Math Team   Joined: Jul 2011 From: Texas Posts: 2,924 Thanks: 1521 $s = 4t+\ln(1-t)$ note the domain of this function is $t < 1$, so finding the value of the derivative at $t = 1.5$ seconds is not possible for real values of $\ln(1-t)$. recheck the problem statement ... could the position function possibly be $s = 4t+\ln|1-t|$ ? fyi ... $\dfrac{ds}{dt} = 4 - \dfrac{1}{1-t} = 4 - (1-t)^{-1}$ $\dfrac{d^2s}{dt^2} = (1-t)^{-2} \cdot (-1) = -\dfrac{1}{(1-t)^2}$ Thanks from topsquark and Country Boy May 22nd, 2017, 08:52 AM #5 Newbie   Joined: Jan 2017 From: brussels Posts: 28 Thanks: 0 Can you show me the first differential in sequence order rather than all in one? I have only done basic differentiation and don't really understand the chain rule. Last edited by skipjack; February 8th, 2019 at 03:38 AM. May 22nd, 2017, 09:15 AM   #6
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Quote:
 I have only done basic differentiation and don't really understand the chain rule
then you should learn the chain rule before continuing ...

Chain Rule Introduction May 22nd, 2017, 01:10 PM #7 Newbie   Joined: Jan 2017 From: brussels Posts: 28 Thanks: 0 Thank you - that link was very helpful. Last edited by skipjack; February 8th, 2019 at 03:20 AM. February 7th, 2019, 08:25 PM #8 Newbie   Joined: Oct 2017 From: Texas Posts: 9 Thanks: 0 I think you should look at the basics first Hello The differentiation done above is absolutely correct. I think if you're having trouble doing differentiation, you should first remember all of its formulas. Keep the formulas handy, and memorized...then everything will turn easier. Here is a good list of Differentiation Formulas Last edited by skipjack; February 8th, 2019 at 03:22 AM. February 8th, 2019, 03:35 AM   #9
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Quote:
 Originally Posted by skeeter ... could the position function possibly be $s = 4t+\ln|1-t|$ ?
That wouldn't help. The question still wouldn't make sense. Tags differentiation Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Mr Davis 97 Calculus 1 March 9th, 2015 04:50 AM Raptor Calculus 2 May 8th, 2014 06:12 AM Thepiman Calculus 1 May 8th, 2014 06:11 AM Raptor Calculus 6 May 7th, 2014 11:33 AM Raptor Calculus 1 May 7th, 2014 07:47 AM

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