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Thread: Derivatives of Logarithmic functions

  1. #1
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    Derivatives of Logarithmic functions

    can someone help me to find the derivative of this function??

    y=ln(x+(x^2+a^2)^1/2)

    I'm not getting the answer 1/(x^2+a^2) from my textbook

    thanks
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  2. #2
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    Quote Originally Posted by Aniff View Post
    can someone help me to find the derivative of this function??

    y=ln(x+(x^2+a^2)^1/2)

    I'm not getting the answer 1/(x^2+a^2) from my textbook

    thanks
    your textbook "answer" is incorrect (unless you forgot an exponent or radical in the denominator) ...

    y' = \dfrac{1 + \dfrac{x}{\sqrt{x^2+a^2}}}{x + \sqrt{x^2+a^2}}

    multiply numerator and denominator by \sqrt{x^2+a^2} to clear the inner fraction in the numerator ...

    y' = \dfrac{\sqrt{x^2+a^2} + x}{(x + \sqrt{x^2+a^2})\sqrt{x^2+a^2}}<br />

    see what happens now?
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  3. #3
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    yeah sorry i missed the sqrt...should be 1/(x^2+a^2)^1/2

    ok I already got to that point but could not simplify any further??
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  4. #4
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    y' = \dfrac{\sqrt{x^2+a^2} + x}{(x + \sqrt{x^2+a^2})\sqrt{x^2+a^2}}<br />

    LOOK again at the factors in the numerator and denominator ...
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  5. #5
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    ooohh okay I can see it now...I can cancel the common factors

    thanks a lot I was blind...lol
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