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Differention using combination of rules help?

  • 22-04-2008 06:42PM
    #1
    Closed Accounts Posts: 96 ✭✭


    while im on here i may as well ask cause
    ive 4 problems using a combination of rules but there really confusing me
    thanks in advance again for any help given

    problem 1
    sin2x/x^2+3x-2

    problem 2
    (3sinx)(x^3+2x+1)^6

    problem 3
    ln(4x^2+2x-1)^3

    problem 4
    tan3x^2(ln(2x-3))^3


Comments

  • Moderators, Science, Health & Environment Moderators Posts: 1,855 Mod ✭✭✭✭Michael Collins


    Should there be brackets in the first one?

    Well taking is as you've written it you use the quotient rule and the chain rule on the first term, and just the usual differentiation rules on the remaining two terms.

    The quotient rules says:

    y(x) = u(x)/v(x)

    y'(x) = [v(x) * u'(x) - u(x) * v'(x)]/ [v(x)]^2

    where the dash (') means differentiation.

    For example take

    y(x) = 3x^2/[4x+1]

    y'(x) = [(4x+1)* 6x - 3x^2 * 4] / [4x]^2 = [12x^2 + 6x] /16x^2

    so apply a similar process to the first one and see how you get on.


  • Registered Users, Registered Users 2 Posts: 1,501 ✭✭✭Delphi91


    ...For example take

    y(x) = 3x^2/[4x+1]

    y'(x) = [(4x+1)* 6x - 3x^2 * 4] / [4x]^2 = [12x^2 + 6x] /16x^2 ...

    Methinks it should be over [4x+1]^2 rather than [4x]^2.


  • Moderators, Science, Health & Environment Moderators Posts: 1,855 Mod ✭✭✭✭Michael Collins


    Yep, thank you.


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