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Differentiation dilemma

  1. Dec 19, 2007 #1
    I'm having trouble with the following questions about differention with respect to x.

    Differentiate with respect to x:

    a)

    y= 2/ (2x+3)^4

    b)

    y= x(x+1)^(1/2)

    c)

    y= (x +1)(x^2 + 3x)^3

    d)

    y= 3x^3 + 3x^(-1/2) + 2



    Any help would be greatful
     
  2. jcsd
  3. Dec 19, 2007 #2
    Have you learned the chain rule yet?
     
  4. Dec 19, 2007 #3

    Hootenanny

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    Re-write as;

    [tex] y = 2(2x+3)^{-4}[/tex]

    And use the chain rule.

    Chain rule and product rule

    Just use the power rule.
     
  5. Dec 19, 2007 #4
    Yes, I have learnt chain rule

    to differentiate from x you find dy/dx
     
  6. Dec 19, 2007 #5
    Here are my solutions, I don;t know if they're correct

    a)

    y= 2/ (2x+3)^4

    = -4(2x +5)^(-5) x 2 x 2

    = -16/ (2x + 5) ^ (-5)

    b)

    y= x(x+1)^(1/2)

    = ( x + 2) (x + 1)^ (1/2) / 2

    d)

    y = 3x^3 + 3x^(-1/2) + 2

    = 3x^2 - 3/2x^(1/3)
     
    Last edited: Dec 19, 2007
  7. Dec 19, 2007 #6

    Hootenanny

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    Almost, where's the +5 come from in the bracket? And are you sure that should be a -5?
    I'm not sure where your coming from with that, perhaps if you posted your steps?
     
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