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Find the first partial derivative of

  1. Oct 3, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the first partial derivatives ∂z/∂x and ∂z/∂y of sin(0x+5y+z)=0 at (0,0,0).

    2. Relevant equations

    sin(0x+5y+z)=0


    3. The attempt at a solution

    0x+5y+z=kπ
    z=kπ-5y

    So,

    ∂z/∂x= 0 and ∂z/∂y= -5

    What I do not understand is WHY 0x+5y+z=kπ is an acceptable equation. I found it from a solution of this online, but with no explanation. What is the significance of k and π, and why can we basically ignore the sin?
     
  2. jcsd
  3. Oct 4, 2013 #2

    Simon Bridge

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    You have the relation ##\sin(\theta)=0:\theta=5y+z## right ... so what values of ##\theta## make the relation true?
     
  4. Oct 4, 2013 #3
    Oh, duh! Sin(0)=0.

    Thanks
     
  5. Oct 4, 2013 #4

    Simon Bridge

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    ##\sin k\pi=0:k=0,1,2,\cdots##
    ... sometimes you are staring right at it.
     
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