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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?
    -3sinx2*2x
    c.) use the quotient rule
    ((5x+2)(2)-(2x-1)(5))/(5x+2)2

    ((10x+2)-(10x-5))/(5x+2)2

    7/(5x+2)2

    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
    2sinxcosx*(-cosxsinx)
     
  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
    3(cos(x[itex]^{2}[/itex]))[itex]^{2}[/itex](-sin(x[itex]^{2}[/itex]))(2x)

    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

    berkeman

    User Avatar

    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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