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Derivatives using chain rule

  1. Jun 12, 2014 #1
    Need to find the Derivative using the chain rule

    y = x2sin4(x) + xcos-2(x)

    I am not sure where to start.

    answer in book is
    2xsin4(x) + 4x2sin3(x)cos(x) + cos-2(x) +2xcos-3(x) xsin(x)
     
  2. jcsd
  3. Jun 12, 2014 #2
    I am not sure if I did it right but I think I got the answer.

    x2sin4(x)
    2xsin4 took derivative of just x2
    4x2sin3x derivative of just power of sin
    cosx derivative of just sin

    2xsin4(x)+4x2sin3(x)cos(x)

    xcos-2(x)

    cos-2 derivative of x
    -2xcos-3(x) derivative of power of cos
    -xsin(x) derivative of just cos

    cos-2+2xcos-3(x)sin(x)

    final answer
    2xsin4(x)+4x2sin3(x)cos(x)+cos-2(x)+2xcos-3(x)xsin(x)
     
    Last edited: Jun 12, 2014
  4. Jun 12, 2014 #3
    Yes, but your work is very strange and hard to read, and I think it makes it more difficult than it should be.

    Also, tidy up your penmanship a bit. sin² doesn't mean anything.

    Just some suggestions.
     
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