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Partial derivatives - textbook error?

  1. Aug 14, 2008 #1
    Now in my textbook it shows the following partial derivative solution:

    [tex]\frac{d}{dx}[/tex](3y[tex]^{4}[/tex] + e[tex]^{x}[/tex] sin y) = e[tex]^{x}[/tex] sin y

    I thought since it's meant to be the partial derivative in terms of x that the y variable would be untouched.

    What's happening?
     
  2. jcsd
  3. Aug 14, 2008 #2
    What's the first derivative of f(x) = 3*(5^4) + e^x * sin(5)?
     
  4. Aug 14, 2008 #3
    e^x ?
     
  5. Aug 14, 2008 #4
    Try again.
     
  6. Aug 14, 2008 #5
    Huh? What else can it be, the rest are all constants.
     
  7. Aug 14, 2008 #6

    Defennder

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    If a constant is multiplied to f(x), it doesn't become 1 after differentiating them both.
     
  8. Aug 14, 2008 #7

    tiny-tim

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    Hi JFonseka! :smile:
    The Chain Rule is happening!

    d/dx(exsiny) = (d/dx(ex)) siny + ex(d/dx(siny)) :smile:
     
  9. Aug 14, 2008 #8
    I get that bit lol, but I don't get why 3y^4 disappeared,
     
  10. Aug 14, 2008 #9
    Nvm I get it now.
     
  11. Aug 14, 2008 #10
    Thanks to all who helped
     
  12. Aug 14, 2008 #11
    I think you mean the product rule?
     
  13. Aug 14, 2008 #12

    tiny-tim

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    :redface: oops! :redface:
     
  14. Aug 14, 2008 #13
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