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Please tell me how they got this derivatives

  1. Oct 4, 2009 #1
    Ok, I need help understanding this really bad. I don't get it. There were examples of derivatives in the book but I don't get how they got the answer. Here were the examples.

    They all said to find the derivatives algebraically.

    f(x)=x[tex]^3[/tex] at x=-2

    The answer was 12.

    f(x)=x[tex]^3[/tex]+5 at x=1

    The answer was 3.

    How did they get these answers, I don't understand it, can someone help explain?
     
  2. jcsd
  3. Oct 4, 2009 #2

    rock.freak667

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    Re: Derivatives?

    ok for f(x)=xn we know that f'(x)=nxn-1

    So in your first example f(x)=x3, so what is n and what is f'(x)? When you find f'(x) just put x=2 into your equation.
     
  4. Oct 4, 2009 #3
    Re: Derivatives?

    Ah, that clears it up. A little confusing but I see that 3(-2)[tex]^3^-^1[/tex]=12

    Thanks.

    But for the second one, are you not supposed to do anything with the +5?
     
  5. Oct 4, 2009 #4
    Re: Derivatives?

    Okay, I have a weird one of this. It says find the derivative of g(x)=1/x at x=2 algebraically. So I got

    g'(x)=1(2)[tex]^1^-^1[/tex] which is 2[tex]^0[/tex] which =1. Right? There were no exponents so I put 1, just want to make sure I am doing this right.
     
  6. Oct 4, 2009 #5

    rock.freak667

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    Re: Derivatives?

    for the second one, f(x)=x3+5, then f'(x)=d/dx(x3)+d/dx(5)

    g(x)=1/x , so we can see this is not in the form xn.But we know a rule in indices that says 1/am=a-m

    So now using this rule what is another way to write 1/x?

    g(x) ?
     
  7. Oct 4, 2009 #6
    Re: Derivatives?

    Ok, so it would be -1(2)[tex]^-^1^-^1[/tex], which is -2^-2 =1/4 right?
     
  8. Oct 4, 2009 #7

    rock.freak667

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    Re: Derivatives?

    remember -ab means you take '-a' and raise it to the power of b

    -(a)b means you take 'a' and raise to the power of 'b' and then multiply by -1
     
  9. Oct 4, 2009 #8
    Re: Derivatives?

    Ok so you mean 2^-1 which is 1/2 and then 1/2(-1) which is -1/2?
     
  10. Oct 4, 2009 #9

    rock.freak667

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    Re: Derivatives?

    no no, you have -(2)-1-1=-(2)-2=-(2-2). So what number do you get now?
     
  11. Oct 4, 2009 #10
    Re: Derivatives?

    -1/4.
     
  12. Oct 4, 2009 #11

    rock.freak667

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    Re: Derivatives?

    and that is correct.
     
  13. Oct 4, 2009 #12
    Re: Derivatives?

    Cool, thanks. I see how that works.
     
  14. Oct 4, 2009 #13
    Re: Derivatives?

    This is false. -ab means -(ab).

    If you meant raising -a to the bth power, you have to write (-a)b.

    --Elucidus
     
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