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Homework Help: Can't solve this simple derivative

  1. Nov 3, 2012 #1
    Can someone please show me how to get the derivative of (-x^2/18). I know the answer is x/9 but I use the quotient rule and keep getting (x^2-36x)/18^2

    Thanks b
     
    Last edited: Nov 3, 2012
  2. jcsd
  3. Nov 3, 2012 #2
    Instead of using the quotient rule, try writing the function as:

    [itex]\frac{1}{18}x^2[/itex]

    Now it is just a power rule derivative. Does that help?

    Not that the quotient rule doesn't work, though. From your answer, it looks like you're doing it incorrectly. Remember that the quotient rule is:
    [tex]\frac{d}{dx}\frac{f(x)}{g(x)}=\frac{g(x)f'(x)-f(x)g'(x)}{(g(x))^2}[/tex]
     
    Last edited: Nov 3, 2012
  4. Nov 3, 2012 #3
    So I did (1/18)(x^2)

    To get 2x(1)+(1/18)(x^2)

    2x+(x^2/18)

    (36x+x^2)/18

    what can i do after that step?
     
  5. Nov 3, 2012 #4
    You're using the power rule incorrectly also. The power rule is:
    [tex]\frac{d}{dx}cx^n=ncx^{n-1}[/tex]Edit: Ah, it looks you are trying to do the product rule. Remember that if you have any constant times x or x divided by a constant, you can use the power rule instead of the product or quotient rules.

    Remember that the derivative of a constant term is 0, not 1!

    Still, once again, the power rule does work in this case. It is:
    [tex]\frac{d}{dx}f(x)g(x)=f'(x)g(x)+f(x)g'(x)[/tex]
     
    Last edited: Nov 3, 2012
  6. Nov 3, 2012 #5
    whoops it should have been -x^2+36x/18^2 for the quotient rule
     
  7. Nov 3, 2012 #6
    Yea thanks I just had a small mental break down was making stupid mistakes
    I get (18x^2+2x)/18
     
  8. Nov 3, 2012 #7
    Let's try this first:

    What is [itex]\frac{d}{dx}x^2[/itex] ?
     
  9. Nov 3, 2012 #8
    it would be 2x
     
  10. Nov 3, 2012 #9

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    What is
    [tex]\frac{d}{dx} \left(\frac{1}{18}\right) \, ?[/tex]

    RGV
     
  11. Nov 3, 2012 #10
    a constant so one
     
  12. Nov 3, 2012 #11
    The derivative of a constant is 0.
     
  13. Nov 3, 2012 #12
    ------
     
  14. Nov 3, 2012 #13
    WOW im such a fool...
     
  15. Nov 3, 2012 #14
    alright I got it now......(2x/18)=x/9

    Thanks everyone for your help much appreciated
     
  16. Nov 3, 2012 #15

    Mark44

    Staff: Mentor

    A couple more points that weren't brought up in this thread:

    1. You should never use the quotient rule if the denominator is a constant. It's not wrong to use the quotient rule, but it's more complicated, which makes it more likely that you will make a mistake.

    For example, if f(x) = x2/4, write this as (1/4)x2 and use the constant multiple rule, which says that d/dx(k*f(x)) = k*d/dx(f(x)).
    Using this rule we get f'(x) = (1/4) * d/dx(x2) = (1/4) * 2x = x/2

    2. You should never use the product rule if one factor is a constant. Instead, use the constant multiple rule. It would not be incorrect to use the product rule, but as before, it's more complicated, so you are more likely to make a mistake.

    For example, if g(x) = 10 * tan(x), then g'(x) = 10 * d/dx(tan(x)) = 10 * sec2(x).
     
  17. Nov 5, 2012 #16
    Thanks that definitely helped me
     
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