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Math Help - first and second derivatives of a function

  1. #1
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    first and second derivatives of a function

    can anyone help me finding first and second derivatives of these functions?

    1) y=ln (x^2 +1)-x

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

    3) y=tan x- x i got up to 2 sec^2xtanx

    4) y=ln (x^2+1)

    thanks lots
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  2. #2
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    Quote Originally Posted by katieeej View Post
    can anyone help me finding first and second derivatives of these functions?

    1) y=ln (x^2 +1)-x

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

    3) y=tan x- x i got up to 2 sec^2xtanx

    4) y=ln (x^2+1)

    thanks lots
    #1 ...

     <br />
\frac{d}{dx} \ln(u) = \frac{1}{u} \cdot \frac{du}{dx}<br />

    #2 ... chain rule

     <br />
\frac{d}{dx} (u)^{\frac{1}{2}} = \frac{1}{2}(u)^{-\frac{1}{2}} \cdot \frac{du}{dx}<br />

    # 3 ...

     <br />
\frac{d}{dx} (\tan{x} - x) = \sec^2{x} - 1 = \tan^2{x}<br />

    #4 ... use the rule given for #1.
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