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Is this proof correct?

  1. Oct 2, 2012 #1
    1. The problem statement, all variables and given/known data

    Using the chain rule, prove that d/dx(cotx)= -csc^2x

    2. Relevant equations

    Chain rule

    3. The attempt at a solution

    Is this correct?

    f(x)=cotx=(tanx)^(-1)
    Let f(x) = (x)^-1 Therefore, f'(x)= -1/(x^2)
    Let g(x) = tanx Therefore, g'(x)= sec^2x

    F'(x)=f'(g(x))g'(x)
    =(-1/(tanx)^2)(secx^2)
    =(-secx^2)/(tanx^2)
    = -csc^2 x
     
  2. jcsd
  3. Oct 2, 2012 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    It's not a good idea to use "x" as the variable here. Use, say, u instead:
    f(u)= u^-1 so f'= -1u^-2.

    Yes, that is a valid proof.
     
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