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!

Partial derivative

  1. Jul 15, 2006 #1
    f( x(1), ......, x(n) ) = sum (i=1) sin(x(i)^2) x(i)

    does anybody knows how to solve this pls
     
  2. jcsd
  3. Jul 15, 2006 #2
    What is this exactly? And what does this have to do with partial derivatives?
     
  4. Jul 15, 2006 #3

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Don't be intimidated by the sum sign. Write what the sum is explicitely and you'll find a more familiar form. Also, you can resolve the special case n=3 and renaming x(1)=1, x(2)=y and x(3)=z first before tackling the more abstract general case of n variables.
     
  5. Jul 16, 2006 #4
    f( x(1), ......, x(n) ) = sin(x(1)^2) x(1) + sin(x(2)^2)x(2) + sin(x(2)^2)x(2) + sin(x(3)^2)x(3) + ...... +sin(x(n)^2)x(n)

    should i write this eqn like this??
     
  6. Jul 16, 2006 #5

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    There's nothing here to "solve".
    You just have a function f, given by the prescription:
    [tex]f(x_{1},\cdots{x}_{n})=\sum_{i=1}^{n}x_{i}\sin(x_{i}^{2})[/tex]
     
  7. Jul 16, 2006 #6
    so u mean i just have to write the eqn above and no need to do partial derivative as the question ask to do so??
     
  8. Jul 16, 2006 #7

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    It isn't an equation, it is a definition of the function f.
     
  9. Jul 16, 2006 #8
    okok......thanx
     
  10. Jul 16, 2006 #9

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Now that you've expanded the sum, it should be easier to see what the derivative wrt x(1) is. (remember, the derivative of a sum is the sum of the derivative)
     
  11. Jul 16, 2006 #10
    f( x(1), ......, x(n) ) = sin(x(1)^2) x(1) + sin(x(2)^2)x(2) + sin(x(2)^2)x(2) + sin(x(3)^2)x(3) + ...... +sin(x(n)^2)x(n)

    so should i write this eqn like this??

    for quasar987
     
  12. Jul 16, 2006 #11

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Again, this isn't an equation, but a definition of a function
    Secondly, try to formulate IN YOUR OWN WORDS what you are supposed to do with this function! (This, you have failed to do so far)
     
  13. Jul 16, 2006 #12
    This form of the expression makes it easier to "find" the derivatives, so I would write the equation this way.
     
  14. Jul 16, 2006 #13

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Can you find the derivative of f(x) = xsin(x²) ?
     
  15. Jul 16, 2006 #14
    i think can by using u'v + vu' formula rite??
     
  16. Jul 16, 2006 #15

    VietDao29

    User Avatar
    Homework Helper

    No, no, no. Another wrong answer. It's uv'. Repeat after me: (uv)' = u'v + uv', (uv)' = u'v + uv'.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Partial derivative
  1. Partial derivative (Replies: 1)

  2. Partial derivative (Replies: 2)

  3. Partial derivatives (Replies: 1)

  4. Partial derivative (Replies: 21)

  5. The partial derivative (Replies: 2)

Loading...