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Differentiable functions of x

  1. Oct 29, 2011 #1
    1. The problem statement, all variables and given/known data
    Suppose u and v are differentiable functions of x. Use the given values of the functions and their derivatives to find the value of the indicated derivative.
    u(1)=2, u'(1)=-7, v(1)=7,v'(1)=-2
    d/dx (uv) at x =1

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Oct 29, 2011 #2


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    What have you tried?
  4. Oct 29, 2011 #3

    Simon Bridge

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    2. Relevant equations
    look for the equations you use when you have to differentiate a combination of two functions... one of them looks like your problem.
  5. Oct 29, 2011 #4
    I get d/x(uv)=(2)(-2) + (7)(-7) = -53 but I'm not applying the 1 anywhere that I know of here. as in u(1), does anyone have an example that could help me?
  6. Oct 29, 2011 #5

    Ray Vickson

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    In your answer (2)(2) + (7)(-7), where did the 2 come from? What about the -2? Where did you get the 7? Ditto for the -7.

  7. Oct 29, 2011 #6
    That answer looks correct to me. You are applying the 1. The equation for the derivative of the product of two functions is u*v' + v*u'. In your case, you have u(1)*v'(1) + v(1)*u'(1) = (2)(-2) + (7)(-7) = -53. This is d/dx(uv) evaluated at x=1.
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