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Math Help - differentiation

  1. #1
    Junior Member mathmonster's Avatar
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    differentiation

    i know this is a simple differentiation, but i just can't remember how to do it!
    can someone please differentiate

    ((x^3)+3(x^2)+1) ^(1/3)

    also how can i write x^2 on this forum so it looks like how x^2 should look, with a superscript 2.
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  2. #2
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    Hello, mathmonster!

    You need the Chain Rule . . .


    f(x) \;=\;\left(x^3+3x^2+1\right)^{\frac{1}{3}}

    f'(x)\;=\;\frac{1}{3}\left(x^3+3x^2+1\right)^{-\frac{2}{3}}(3x^2 +\, 6x) \;=\;\frac{3x^2+6x}{3(x^3+3x^2+1)^{\frac{2}{3}}} \;=\;\frac{x^2+2x}{(x^3+3x+1)^{\frac{2}{3}}}

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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by mathmonster View Post
    also how can i write x^2 on this forum so it looks like how x^2 should look, with a superscript 2.
    Left-click on the script that Soroban wrote in his answer. That will show you how to code it.

    There is a thread on how to use LaTeX in one of the subforums. (Or you could do a web search. Tips on how to code are all over it.)

    -Dan
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  4. #4
    Junior Member mathmonster's Avatar
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     <br />
\log_{5} 25=2<br />
    just checking now to see how this works
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  5. #5
    Junior Member mathmonster's Avatar
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     <br />
f(x) = (x^3+3x^2+1)^{\frac{1}{3}}<br />
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by mathmonster View Post
     <br />
f(x) = (x^3+3x^2+1)^{\frac{1}{3}}<br />
    Looks like you've got it!

    -Dan
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