1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Urgend Calculus Question: Please Look

  1. Sep 24, 2006 #1
    Hi

    Given [tex]z = sin(x + sin(t))[/tex]

    show that [tex]\frac{\partial z}{\partial x} \cdot \frac{\partial ^2 x}{\partial x \partial z} = \frac{\partial z}{\partial t} \cdot \frac{\partial ^2 z} {\partial x^2}[/tex]

    By using the chain-rule I get:

    [tex]f_x(x,t) = cos(x + sin(1))[/tex]

    [tex]f_{xx}(x,t) = -sin(x + sin(1))[/tex]

    [tex]f_t(x,t) = cos(1) \cdot cos(x + sin(1))[/tex]

    [tex]f_{tt}(x,t) = 0[/tex]

    Therefore

    [tex]\frac{\partial z}{\partial x} \cdot \frac{\partial ^2 x}{\partial x \partial z} = cos(x + sin(1)) \cdot 0 = cos(1) \cdot cos(x + sin(1)) \cdot 0 = \frac{\partial z}{\partial t} \cdot \frac{\partial ^2 z} {\partial x^2}[/tex]

    Does that look right ?

    Sincerely
    MM20
     
    Last edited: Sep 24, 2006
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted