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Dervite a function

  1. Mar 29, 2008 #1
    Derivating a function of a function with two variables

    Hi i am new to this forum so please bear with me if i made a mistake or posted in the wrong section :)

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

    Given that f(x,y)= ((x^-1)+(y^-1)) find F'x and F'y
    Given z= F(x,y) and x=f(t) while y= g(t,s) express dz/dt and dz/ds

    2. Relevant equations

    This i hope you can help me with, missed the lecture where the professor explained this and i can't find any relevant information in the math book nor did googling or wikipedia help.

    3. The attempt at a solution

    This is the first time i encounter derviation of functions, I have no problems derivating equations and most of my life i just had to derivate X, this is why i have no clue as to how i should solve this problem.

    F'x= -1/(x)^2 and F'y= -1/(y)^-2

    I hope you can explain it to me instead of just giving an answer and i will be grateful.


    Thanks for your help and sorry for the bad english

    Edit: Even the name of the subject this problem touches would be ok, and hopefully some links :D more fun that way
     
    Last edited: Mar 29, 2008
  2. jcsd
  3. Mar 29, 2008 #2

    HallsofIvy

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    Science Advisor

    You are dealing with partial derivatives since F depends upon two independent variables.
    What you are calling "F'x" and "F'y" would be more properly called [itex]\partial F/\partial x[/itex] and [itex]\partial F/\partial y[/itex] or just Fx and Fy, respectively.

    The partial derivative of a function, with respect to x, is jus the derivative treating y as a constant. What is dF/dx if F(x)= x-1+ C for some constant C? What is dF/dy if F(y)= C+ y-1?
     
  4. Mar 30, 2008 #3
    Thank you so much, i am gonna try and find relevant information on this subject and learn it by myself :) thanks again. I will solve the querstions you asked in a few hours, have to eat first.
     
  5. Mar 30, 2008 #4
    Allright for the second part of the problem i have that z = F(x,y)= F(f(t), g(t,s))

    I understand that dz/dt= F'x(x,y)dx/dt + F'y(x,y)dy/dt

    But what about dz/ds, how do i proceed there?

    Edit:

    seeing as s isn't a function of f(x)=x is x a constant when you derivate dz/ds? If x is a constant, would the correct answer be

    dz/ds= F'y(x,y)(dy/ds)?
     
    Last edited: Mar 30, 2008
  6. Mar 30, 2008 #5
    Hey
    Yes it is correct. As x has no dependence on s
    [tex]\frac{\partial{x}}{\partial{s}}=0[/tex]
     
  7. Mar 30, 2008 #6
    Thank you :)

    Edit: How do you guys manage to write the symbols in here? Html code?
     
    Last edited: Mar 30, 2008
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