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 (1t) 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 (1t) 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?

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 
$s = 4t+\ln(1t)$ 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 $\ln(1t)$. recheck the problem statement ... could the position function possibly be $s = 4t+\ln1t$ ? fyi ... $\dfrac{ds}{dt} = 4  \dfrac{1}{1t} = 4  (1t)^{1}$ $\dfrac{d^2s}{dt^2} = (1t)^{2} \cdot (1) = \dfrac{1}{(1t)^2}$ 
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  
Math Team Joined: Jul 2011 From: Texas Posts: 2,924 Thanks: 1521  Quote:
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 
Global Moderator Joined: Dec 2006 Posts: 20,633 Thanks: 2080  

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