Differentiation

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  1. Vadevalor's Avatar
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    Differentiation
    What is wrong with my steps:0 cant get the answer 1/ (sq root(x2 +a2))


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  2. nuodai's Avatar
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    Re: Differentiation
    You made your life instantly harder when you went from your third line to your fourth line.

    Write 1 + \dfrac{x}{\sqrt{x^2+a^2}} = \dfrac{x + \sqrt{x^2+a^2}}{\sqrt{x^2+a^2}}, i.e. just put it over the common denominator, and the path is clear from there.

    If you want to carry on with your own method, take \sqrt{x^2+a^2} out as a common factor in the denominator (on the last line of your working) and simplify the resulting fraction. You didn't do anything wrong, you just made it harder than it had to be!
    Last edited by nuodai; 19-07-2012 at 13:24.
  3. Vadevalor's Avatar
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    Hmmm I did that and arrived here, cant seem to get the answer with my workings though so thought its wrong cant seem to simplify fraction to have denominator sq root(x2+a2)


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  4. nuodai's Avatar
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    Re: Differentiation
    (Original post by Vadevalor)
    Hmmm I did that and arrived here, cant seem to get the answer with my workings though so thought its wrong cant seem to simplify fraction to have denominator sq root(x2+a2)
    You've made a mistake there by saying that \dfrac{1}{x+\sqrt{x^2+a^2}} = \dfrac{1}{x} + \dfrac{1}{\sqrt{x^2+a^2}}. This is not true.

    If you did as I said, you'd get

    \dfrac{1}{x+\sqrt{x^2+a^2}} \cdot \dfrac{x+\sqrt{x^2+a^2}}{\sqrt{x  ^2+a^2}}

    How might you simplify this?
  5. raheem94's Avatar
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    Re: Differentiation
    (Original post by Vadevalor)
    Hmmm I did that and arrived here, cant seem to get the answer with my workings though so thought its wrong cant seem to simplify fraction to have denominator sq root(x2+a2)


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    Continuing your first attempt,
     \displaystyle \frac{x+ \sqrt{x^2+a^2}}{x \sqrt{x^2 + a^2 } + x^2 +a^2 } = \frac{x+ \sqrt{x^2+a^2}}{x \sqrt{x^2 + a^2 } + (x^2 +a^2) }  = \frac{(x+ \sqrt{x^2+a^2})}{\sqrt{x^2+a^2} ( x + \sqrt{x^2+a^2} )}
  6. Vadevalor's Avatar
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    Re: Differentiation
    thanks both of you! i couldnt get what's the difference since i'm still gonna combine it all into a single fraction hehe. But raheem was spot on! factorising.. i cant believe i missed that out!
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