First & Second derivative of a function

  1. 1. The problem statement, all variables and given/known data
    The function Sh(t) = 30[cos(16.04*)]t models the horizantal position of a pellet with respect to time.

    Find the first & second derivatives of Sh(t).



    2. Relevant equations


    3. The attempt at a solution I attached a word document because I lack the ability to put together a correctly formatted latex doc in my post. I apologize for the inconvenience. Thank you in advance.

    Joe


    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Sh(t) = 30[cos(16.04*)]t
    1st derivative 30cos(16.04)
    2nd 0
    If the t is in the cos function, then
    1st 16.04*30*(-sin16.04t)
    2nd 16.04^2*30*(-cos16.04t)
     
  4. vela

    vela 12,443
    Staff Emeritus
    Science Advisor
    Homework Helper

    The first term in the numerator of your limit should be [itex]30(\cos 16.04^\circ)(t+\Delta t)[/itex], so [itex]\Delta t[/itex] gets multiplied by the constant.
     
  5. I didn't download the paper. I just responded to what the derivatices would be based on what is giving. You need to do the limit definition to obtain the derivatives?
     
  6. So for my first derivative I get to an answer of delta t/delta t, which I'm sure isn't correct. Are there some rules for differentiating when trig functions are involved that differs from a function say f(x)=x^3 ? Also I posted this question incorrectly as I was going off memory the first time. In the real problem there is no limit written next to the function, does this change things at all? I figured that equation without a limit is just the slope of a secant line. Thanks in advance.

    Joe
     
    Last edited: Feb 8, 2010
  7. Re: First & Second derivative of a function [Solved]

    I figured it out. I was missing some rules for derivatives such as f(x)= a constant * a variable, then f'(x) =the constant. Another one was f'(x) of a constant =0. This is of course what Dustin was trying to tell me, I just couldn't put it together from that context. Thanks for your help gentlemen.

    Joe
     
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