Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How do you get the derivative of this?

  1. Sep 6, 2006 #1
    This is for my Circuits class, I am supposed to find the current i.

    If q = 5te^(-10^(3) t) Coulombs

    Find i (current) the formula for i is: i = dq/dt

    So what I did was try to find the derivative of q, which is dq

    So I brought out the constant 5, and I am left with te^(-10^(3) t)

    and I recognize this as a product of two functions so I tried the product rule.

    I let my first function f = t, and my second function g = e^(-10^(3) t)

    so f ' = 1 and g ' (using the chain rule) i got (e^(-10^(3) t) x '10^3)

    so i plugged it into the product role (fg)' = fg' + gf' and i get a weird answer.

    The given answer in the back of the book is :

    i = 5(1-10^3 t)e^(-10^3 t) Amps

    can someone help me please
  2. jcsd
  3. Sep 6, 2006 #2


    User Avatar
    Homework Helper

    Perhaps you just need to simplify? What does your current answer look like?

    PS: we have a homework section :wink:
  4. Sep 6, 2006 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Your general approach is correct. g' = e^(-10^(3) t) * -10^3

    When you plug this into the product rule, you get a "weird answer?" Are you sure that your weird answer is not, in fact, the correct answer in unsimplified form?

    - Warren
  5. Sep 6, 2006 #4

    George Jones

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    It looks to me that if you make a small correction in your calculation of g', then you will get the same answer as the book.
  6. Sep 6, 2006 #5


    User Avatar
    Science Advisor

    I presume that is a typo and it should be (e^(-10^(3)t) x (-10^3)) not

    How weird? You just said [itex]f= t, g'= -10^3 e^{-10^3t}, g= e^{-10^3t}, f'= 1[/itex] so [itex]fg'+ f'g= -10^3 te^{-10^3t}+ e^{-10^t}[/itex]
    What do you get if you factor [itex]e^{-10^3 t}[/itex] out of that?

    Last edited by a moderator: Sep 6, 2006
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook