1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Derivative of a surd containing exponential sum

  1. Mar 4, 2012 #1
    1. The problem statement, all variables and given/known data
    y = sqrt(exp(x) - exp(-x))


    2. Relevant equations
    dy/dx = dy/du.du/dx - chain rule
    d/dx(exp(x)) = exp(x) - derivative of exp(x)


    3. The attempt at a solution

    y = sqrt(exp(x) - exp(-x))
    y' = (1/2).(1/sqrt(exp(x) - exp(-x))).[exp(x) - (exp(-x).-1)]

    y' = [exp(x) + exp(-x)]/[2*sqrt(exp(x) - exp(-x))]

    i've tried logarithmic differentation aswell coming up with the same answer. derivative calculator says different. please help
     
  2. jcsd
  3. Mar 4, 2012 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Hello basher87. Welcome to PF !

    What does the derivative calculator say ? Something with cosh and tanh functions ?
     
  4. Mar 4, 2012 #3
    thankyou sammy

    no it comes up with this.

    i have checked the hyperbolic functions, in fact i just substituted 2sinhx for exp(x) - exp(-x)

    and got the same answer

    (exp(-x)*(exp(2.5x) + exp(.5x)))/2(sqrt(exp(2x) - 1) is what the calculator gives
     
  5. Mar 4, 2012 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Is that possibly equivalent to your answer?
     
  6. Mar 4, 2012 #5
    i solved the equation in terms of the hyperbolic function.

    y = sqrt(2sinh x), the derivative calculator gave te same output.

    if i solve it in terms of the exponential equation i get the equivalent but the calculator doesnt. Is it possible that it is a syntax error
     
  7. Mar 5, 2012 #6

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    [itex]\displaystyle \frac{e^{-x}(e^{2.5x} + e^{0.5x})}{2\sqrt{e^{2x} - 1}}[/itex]

    [itex]\displaystyle =\frac{e^{-x}e^{1.5x}(e^{x} + e^{-x})}{2\sqrt{e^{2x} - 1}}[/itex]

    [itex]\displaystyle =\frac{e^{x} + e^{-x}}{2e^{-0.5}\sqrt{e^{2x} - 1}}[/itex]

    [itex]\displaystyle =\frac{e^{x} + e^{-x}}{2\sqrt{e^{x} - e^{-x}}}[/itex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Derivative of a surd containing exponential sum
  1. Exponential Derivative (Replies: 7)

  2. Exponential sum (Replies: 1)

Loading...