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Math Help - Derivative HELP!!

  1. #1
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    Derivative HELP!!

    use logarithmic differentiation to find the derivative of the function:

    y=(tanx)1/x


    the answer is (tanx)1/x(sec2x/xtanx - lntanx/x2)

    but how did they get to that answer i dont understand?
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  2. #2
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    Re: Derivative HELP!!

    What have you tried?

    start by taking the log of both sides. Use the fact that \log_ab^c = c \log_ab

    Good reading is here

    Logarithmic Differentiation
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  3. #3
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    Re: Derivative HELP!!

    Hello, pnfuller!

    Use logarithmic differentiation to find the derivative of the function:

    . . y\:=\:(\tan x)^{\frac{1}{x}}
    Answer: . y' \;=\;(\tan x)^{\frac{1}{x}}\left[\frac{\sec^2x}{x\tan x} - \frac{\ln(\tan x)}{x^2}\right]

    but how did they get to that answer . . . i dont understand?

    What part don't you understand?
    What did you get for your answer? .And how did you get it?

    Have you EVER done any logarithmic differentiation?
    If not, you need more help than we can offer.

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  4. #4
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    Re: Derivative HELP!!

    i have not done logarithmic differentiation so i dont know where to start?
    Quote Originally Posted by Soroban View Post
    Hello, pnfuller!


    What part don't you understand?
    What did you get for your answer? .And how did you get it?

    Have you EVER done any logarithmic differentiation?
    If not, you need more help than we can offer.

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  5. #5
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    Re: Derivative HELP!!

    Quote Originally Posted by pnfuller View Post
    i have not done logarithmic differentiation so i dont know where to start?
    Then have you done implicit differentiation before? If so, that makes things a lot easier. If not, you need to use the chain rule after a transformation.
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