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Math Help - first and second derivatives of the function

  1. #1
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    first and second derivatives of the function

    Find both the first and second derivatives of the the function:
     f(x) = tan^-1 3x
    I started by doing
    dy/dx = 3* 1/1+(3x)^2
    Then 3/(1+9x^2)
    Can anyone finish this off for me please.
    Thanks in advance
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  2. #2
    MHF Contributor Amer's Avatar
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    f(x)=tan^-1(u(x))

    f '(x)=\frac{u'(x)}{1+u^2(x)}

    f''(x)=\frac{(1+u^2)u''(x) - (u'(x))(2u'(x)u(x))}{(1+u^2(x))^2}<br /> <br /> <br /> <br />
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  3. #3
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    Another way to get the second derivative is to write
    [/tex]f'(x)= 3(1+ 9x^2)^{-1}[/tex] and use the power rule and chain rule.
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  4. #4
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    f(x)=tan^-1(3(x))

    f '(x)=\frac{3(x)}{1+3^2(x)}

    Is that correct?
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  5. #5
    MHF Contributor Amer's Avatar
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    no

    f(x) = tan^{-1} 3x

    f'(x)= \frac{3}{1+(3x)^2} = 3(1+9x^2)^{-1}

    f''(x)=-3(18x)(1+9x^2)^{-2}=\frac{-3(18x)}{(1+9x^2)^2}<br />
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  6. #6
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    Thanks for that
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