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Math Help - can't differentiate my own equation!

  1. #1
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    can't differentiate my own equation!

    hello all, i am in year 12 now and trying to differentiate an equation as proof that my thesis on traffic flow is accurate.
    problem is i can't seem to differentiate it.

    equation: Y=(1000x)/(4+(0.2x+0.001x^2))

    i used some online ones but they wouldn't help me..

    if you could attemp to work out Dy/Dx for me i would greatelly appreciate it!
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  2. #2
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by corey0422622443 View Post
    hello all, i am in year 12 now and trying to differentiate an equation as proof that my thesis on traffic flow is accurate.
    problem is i can't seem to differentiate it.

    equation: Y=(1000x)/(4+(0.2x+0.001x^2))

    i used some online ones but they wouldn't help me..

    if you could attemp to work out Dy/Dx for me i would greatelly appreciate it!
    I'll start you off

    y = \frac{1000x}{4+.2x+.001x^2}

    \ln{y} = \ln{\frac{1000x}{4+.2x+.001x^2}}

    \ln{y} = \ln{1000x} - \ln{(4+.2x+.001x^2)}

    \frac{y'}{y} = \frac{1000}{1000x} - \frac{.2 + .002x}{4 + .2x + .001x^2}
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  3. #3
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    earboth's Avatar
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    Quote Originally Posted by corey0422622443 View Post
    hello all, i am in year 12 now and trying to differentiate an equation as proof that my thesis on traffic flow is accurate.
    problem is i can't seem to differentiate it.

    equation: Y=(1000x)/(4+(0.2x+0.001x^2))

    i used some online ones but they wouldn't help me..

    if you could attemp to work out Dy/Dx for me i would greatelly appreciate it!
    Use quotient rule:

    f(x)=\dfrac{h(x)}{g(x)}~\implies~f'(x)=\dfrac{g(x) \cdot h'(x)- h(x) \cdot g'(x)}{(g(x))^2}

    With your problem you'll get:

    y = f(x)= \frac{1000x}{4+0.2x+0.001x^2}

    f'(x)= \frac{1000 \cdot (4+0.2x+0.001x^2) - 1000x \cdot (0.2+ 0.002x)}{(4+.2x+.001x^2)^2}

    Expand the brackets in the numerator only.

    f'(x)= \frac{4000-x^2}{(4+.2x+.001x^2)^2}
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