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Math Help - Help required: 1st and 2nd derivatives of functions

  1. #1
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    Help required: 1st and 2nd derivatives of functions

    Im struggling with finding the 1st and 2nd derivatives of these functions

    f(x)= tan^-1 3x

    So far i have done:
    dy/dx = 3 (1/1+(3x)^2) = 3/ (1+9x^2)

    Im not sure where to go from there
    Any help much appraciated.
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  2. #2
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    Quote Originally Posted by jamm89 View Post
    Im struggling with finding the 1st and 2nd derivatives of these functions

    f(x)= tan^-1 3x

    So far i have done:
    dy/dx = 3 (1/1+(3x)^2) = 3/ (1+9x^2)

    Im not sure where to go from there
    Any help much appraciated.
    Use the chain rule on 3(1+9x^2)^{-1} to find \frac{d^2y}{dx^2}
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  3. #3
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    (3+27x^2)^{-1} so i use chain rule on this?

    u= 3+27x^2 y= u^-1
    du/dx = 54x dy/du= -u^-2

    Can someone finish this off for me please as i have no idea where to go from here
    thanks
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  4. #4
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    Quote Originally Posted by jamm89 View Post
    (3+27x^2)^{-1} so i use chain rule on this?

    u= 3+27x^2 y= u^-1
    du/dx = 54x dy/du= -u^-2

    Can someone finish this off for me please as i have no idea where to go from here
    thanks
    y'' = -3(1 + 9x^2)^{-2} 18x
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