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How to derivative

  1. Dec 18, 2007 #1
    1. The problem statement, all variables and given/known data

    What is the derivative of sin^2(pie*Z) with respect to Z

    2. Relevant equations

    3. The attempt at a solution

    I think the answer is pie/2*sin(pie*Z)

    Is this correct? I keep getting confused with whether or not I should involve the 2 or not of should just leaving it along and just focus on my angle, Z
  2. jcsd
  3. Dec 18, 2007 #2
    sin^2(pie*Z) is sin[tex]^{2}[/tex]([tex]\pi[/tex]z)?
    If it is, Then can't you use the chain rule? which is power rule on the whole out side of the ( ) and then it by multiply by the derivatives of the inside of the ( ). because sin[tex]^{2}[/tex]([tex]\pi[/tex]z) is just the same as (sin([tex]\pi[/tex]z))[tex]^{2}[/tex]
    Last edited: Dec 18, 2007
  4. Dec 18, 2007 #3
    [tex](\sin{x})^2 = \sin^{2}x[/tex]
  5. Dec 18, 2007 #4
    yeah, so Use the chain rule. Look at it as (sinx)^2 because is easier if you look at it like this.
  6. Dec 18, 2007 #5
    no pie is inside the paranthesis next to Z. I was thinking of doing the chain rule but wasnt sure. but its sin -square and the angle is pie next to Z

    Is the answer sin over two *pie
  7. Dec 18, 2007 #6
    [tex]\frac{d}{dz}\sin^{2}{(\pi Z)}[/tex]
  8. Dec 18, 2007 #7
    no, chain rule?
  9. Dec 19, 2007 #8
    hm..I believe the derivative of sin is cos. so the answer should be 2cos(pi*Z) * (Pi) or 2[tex]\pi[/tex]cos([tex]\pi[/tex]Z).

    the first part is power rule and derivative of the Sin which is Cos. for the inside of the ( ), since it's product of a variable and a constant, we know that Pi is a number hence it a constant. So you take the dervitive of pi*Z and use the product rule:
    it will be
    Pi*1 + Z*(0)=Pi.
  10. Dec 21, 2007 #9
    chain rule.

    >_> just do the derivative of x^2 with respect to x [x=sin(pi z)] (the deravative is 2x). After that multiply by the derivative of x with repect to z. d/dz (sin(pi z)) = pi cos(pi z).

    and this is: 2 pi sin(pi z)cos(pi z) and I think thats also equal to pi sin(2pi z) by trigonomtric identities, but not sure about that.
  11. Dec 22, 2007 #10
    never mind this post
  12. Dec 22, 2007 #11
    NO product rule! [itex]\pi[/itex] is NOT a variable, it is a constant just like 2 or [itex]\frac{3}{4}[/itex] or any other NUMBER.

    The chain rule qualitatively says: Take the derivative of the 'outside function' with the inside function as its argument and multiply it times the derivative of the 'inside function'.

    In this case there are 2 outside functions. Start with the squared function and work your way inwards.

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