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Power rule and product rule problem

  1. Jan 27, 2005 #1
    [tex](2x+3)^3(x-4)[/tex]
    How do I differentiate this?
     
  2. jcsd
  3. Jan 27, 2005 #2
    Use the product rule: [itex] vdu + udv [/itex]. For the first function use the power rule: [itex] x^n = nx^{n-1} \frac{du}{dx}=(3(2x+3)^2(2) [/itex]
     
    Last edited: Jan 27, 2005
  4. Jan 27, 2005 #3
    Ok. Thanks!
     
  5. Jan 27, 2005 #4
    [tex]\frac{dy}{dx}=3(2x+3)^2(2) + 1[/tex]
    Right?
     
  6. Jan 27, 2005 #5

    arildno

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    No!
    You must be more careful!
    Define:
    [tex]f(x)=(2x+3)^{3},g(x)=(x-4)[/tex]
    Then,
    [tex]y(x)=f(x)g(x),y'(x)=f'(x)g(x)+f(x)g'(x)[/tex]
    You need therefore to calculate f'(x) and g'(x)
     
  7. Jan 27, 2005 #6
    I got it! Thank you!
     
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