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Homework Help: Finding more derivatives

  1. Nov 13, 2011 #1
    1. The problem statement, all variables and given/known data

    a.) f(x)=tan2(x)

    b.) cos3(x2)

    c.) (2x-1)/(5x+2)

    d.) (sqrt(x2-2x))(secx)

    e.) f(x)=((2x+3)/(x+7))3/2

    f.) [sin(x)cos(x)]2
    2. Relevant equations
    chain rule
    Product rule
    Quotient rule
    Power rule

    3. The attempt at a solution
    a.) would you do the power rule for this? 2tanx
    b.) this is a combination of the chain rule and the power rule?
    c.) use the quotient rule



    d.) use the chain rule and the product rule?
    Use the chain rule for the first pararenthasis. And then use the product rule?
    f.) used the chain rule
  2. jcsd
  3. Nov 13, 2011 #2
    a) this is actually both chain and product rule. tan[itex]^{2}[/itex]x is the same as (tanx)[itex]^{2}[/itex].
    So now you use power rule on the entire function, multiplied by the derivative of the function, i.e. 2tanxsec[itex]^{2}[/itex]x

    b) Again, chain rule and power rule. cos[itex]^{3}[/itex](x[itex]^{2}[/itex]) can be rewritten as (cos(x[itex]^{2}[/itex]))[itex]^{3}[/itex], which, when differentiated, becomes

    c) Looks right

    d) yes

    e) Combination quotient rule / power rule / chain rule. first differentiate as if it were a single variable, then differentiate what's inside using quotient rule.

    f) the first part looks right, 2sinxcosx, but the 2nd part doesn't. The 2nd part should basically be (d/dx)(sinxcosx) which is product rule, i.e. cos[itex]^{2}[/itex]x - sin[itex]^{2}[/itex]x
  4. Nov 13, 2011 #3
    thank you.
  5. Nov 13, 2011 #4


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    Staff: Mentor

    Don't provide solutions here in the future. It violates the PF rules that you agreed to when you joined here.
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