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Find an equation of the line tangent

  1. Sep 6, 2007 #1
    1. The problem statement, all variables and given/known data

    f(x) = |sinx| for - π ≤ x ≤ π
    g(x) = x^2
    h(x)= g(f(x))

    1. Find domain and range of h(x)
    2. Find an equation of the line tangent to the graph of h at the point where x= π/4

    2. Relevant equations

    3. The attempt at a solution

    It think that h(x) is (|sin x|)^2

    so, is domain - π ≤ x ≤ π

    here is where I am confused:

    if d/dx (sin x) = cos x


    is d/dx (|sin x|)^2 = (|cos x|)^2 ?

    thanks in advance for the help.
  2. jcsd
  3. Sep 6, 2007 #2


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    Gold Member

    You cant do that. You should consider using the chain rule.
  4. Sep 6, 2007 #3
    is there any rule for the derivate for an absolute value?
  5. Sep 6, 2007 #4


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    Science Advisor
    Homework Helper

    Squaring makes it easy to answer. |f(x)|^2=f(x)^2. Otherwise you have to split it into subdomains where f(x)>=0 and f(x)<0.
  6. Sep 7, 2007 #5


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    Staff Emeritus
    Science Advisor

    |x|= x if [itex]x\ge 0[/itex], -x is x< 0. Its derivative is 1 if x> 0, -1 if x< 0, not defined for x=0.
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