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Derivative of a composite function

  1. Dec 8, 2013 #1
    y =f(x), and y'=df(x)/dx, F(y)=y^3+(y')^2
    how to deal with the (y')^2 when i calculate dF(y)/dy?
    thanks.
     
  2. jcsd
  3. Dec 8, 2013 #2
    Do you remember the chain rule? Are you having trouble differentiating that term?
     
  4. Dec 8, 2013 #3

    HallsofIvy

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    If u(x) is a fuction of x, then, by the chain rule, the derivative of [itex]u^2[/itex] is 2u times the derivative of u.

    If y is a function of x, then the derivative of [itex](y')^2[/itex], with respect to x, is [itex]2y'[/itex] times the derivative of y' which is, of course, y''. That is, the derivative if [itex](y')^2[/itex] is [itex]2y' y''[/itex].
     
  5. Dec 8, 2013 #4
    HallsofIvy, i want to calculate dF(y)/dy, not dF(y)/dx, but you remand me sth. thank you.
     
  6. Dec 9, 2013 #5

    HallsofIvy

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    Well, that doesn't require any mention of x at all then! The derivative of [itex]d(y)^2/dy= 2y[/itex].
     
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