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Year 11 Double variable derivatives

  1. Aug 14, 2011 #1
    URGENT !!!Year 11 Double variable derivatives

    I am having trouble with this question it is derivatives. Previously I have been able to complete these with no trouble but am a little confused with how start this one:
    y= a^2(3x+5)^3.

    I don't know whether to use the product rule and just leave it with two unknown variables or try and find a value for both a and x.

    I tried this :
    u= a^2
    u'= 2a
    v=(3x+5)^3
    v= 9(3x+5)^2
    y'= v'u +u'v
    = 9a^2(3x+5)^2 + 2a(3x+5)^3
    =a(3x+5)^2[2(3x+5) +9a)]
    =a(3x+5)^2(6x+5+9a)

    Help me please
     
  2. jcsd
  3. Aug 14, 2011 #2
    Re: URGENT !!!Year 11 Double variable derivatives

    Is 'a' a variable or a constant?
     
  4. Aug 14, 2011 #3
    Re: URGENT !!!Year 11 Double variable derivatives

    I have no idea :( I am so lost and i need it for tomorrow :/ it's just basic differential calculus. what would you do?
     
  5. Aug 14, 2011 #4
    Re: URGENT !!!Year 11 Double variable derivatives

    I think it's a constant, meaning that y = f(x) :).
    Then you just treat 'a' as a number.
    Think you can do it from here?
     
  6. Aug 14, 2011 #5
    Re: URGENT !!!Year 11 Double variable derivatives

    Ok um can you guide me through it ?
     
  7. Aug 14, 2011 #6
    Re: URGENT !!!Year 11 Double variable derivatives

    Well, since a^2 is just a number, you don't have to do anything with it.
    So what's the derivative of (3x+5)^3 ?
     
  8. Aug 14, 2011 #7
    Re: URGENT !!!Year 11 Double variable derivatives

    so it would be 9(3x+5)^2? is the working i did at the top correct ? btw thanks heaps for your help
     
  9. Aug 14, 2011 #8
    Re: URGENT !!!Year 11 Double variable derivatives

    Sure, no problem. Yeah it's right :) then that times a^2
     
  10. Aug 14, 2011 #9
    Re: URGENT !!!Year 11 Double variable derivatives

    does that mean I dont need to use the derivative of a^2
     
  11. Aug 14, 2011 #10
    Re: URGENT !!!Year 11 Double variable derivatives

    Yes, because you're taking the derivative with respect to x. 'a' isn't a function of x, so the derivative of 'a' is simply 0.
    So the whole derivative is 9a^2(3x+5)^2.
     
  12. Aug 14, 2011 #11
    Re: URGENT !!!Year 11 Double variable derivatives

    Ohh thanks Lol I understand now!! :)
     
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