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Differentiating twice with respect to x

  1. Mar 6, 2012 #1
    1. The problem statement, all variables and given/known data

    Differentiate twice: z = sinx

    2. Relevant equations

    Product rule
    Chain rule

    3. The attempt at a solution

    dy/dx = dy/dz * dz/dx

    dy/dx = dy/dz * cosx

    Using the product rule:

    d^2y/dx^2 = d^2y/dz^2 * cosx - dy/dz * sinx

    According to the answer in the book the answer is: d^2y/dx^2 = d^2y/dz^2 * cos^2x - dy/dz * sinx but I don't see how.

    Thanks for any help.
  2. jcsd
  3. Mar 6, 2012 #2


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    Science Advisor

    Why are you considering the product and chain? Product is used when you find the derivative of a product f.g , and chain is used when you have an expression f(g(x)),
    and I don't see how you have either of these.
  4. Mar 6, 2012 #3
    Ok. You're right that I don't use the chain rule but the product rule is used when differentiating dy/dx = dy/dz * cosx since theres 2 parts which both have variables.
  5. Mar 6, 2012 #4

    Ray Vickson

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    Science Advisor
    Homework Helper

    You need to be more careful when posing questions. The question you wrote has no y in it anywhere. Did you mean "find d^y/dx^2, when y = f(z) and z = sin(x)"?

  6. Mar 6, 2012 #5
    I think I do. This is part of a much larger second order differential equations question where z = sin(x) is a substitution.
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