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Differentiating composite functions

  1. Oct 22, 2005 #1
    i have bee strugglignwith thes ethree questions for some time now done the 1st one like 8 times :S
    rewrite each of the following in the form y=u^n or y=ku^n, and then differntiate
    1) y = ((1 + x^1/2)/ x^2/3))^3
    i started this by doing writing it out as y = [(1+x^1/2)(x^-2/3)]^3
    then i went did dy/dx = 3[(1+x^1/2)(x^-2/3)]^2[(1/2x^-1/2)(x^-2/3) + (1+x)(-2/3x^-5/3)]
    after simplifying soem i get... 3(1+x^1/2)^2(x^-4/3)(1/2x^1/3-2x^-5/3-2/3x^-2/3)
    ok then i get
    3x^-4/3(1+2x^1/2 + x)(1/2x^1/3-2x^-5/3-2/3x^-2/3)
    Differentiate each function. Express your answer in a simplified factored form.
    2) f(x) = (x+4)^3 (x-3)6
    3) g(x) = (2x-1)^4 (2-3x)^4
    Btw the questions are from the Harcourt Mathematics 12, Advanced Functions & Introductory Calculus, Chapter 4.6 questions 3i, 4a, 4c
    the answers ar in teh abck and i havent even ocme close to the right ones :(
    Thanks in advance
    Also is there an easier way to type this up?
    Last edited: Oct 22, 2005
  2. jcsd
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