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Math Help - derivatives (division and chain rule)

  1. #1
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    Red face derivatives (division and chain rule)

    y=(4x^2+1)^8/12x^3-1

    I know that to start I must set y= u^8 and u= 4x^2+1

    I must then use the quotient rule somehow...

    Thanks so much for any and all help!
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  2. #2
    Senior Member DeMath's Avatar
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    Quote Originally Posted by dogmom09 View Post
    y=(4x^2+1)^8/12x^3-1

    I know that to start I must set y= u^8 and u= 4x^2+1

    I must then use the quotient rule somehow...

    Thanks so much for any and all help!
    Hint:

     y= \frac{{{{\left( {4{x^2} + 1} \right)}^8}}}{{12{x^3} - 1}}.

    \frac{{dy}}<br />
{{dx}} = \frac{{\left( {12{x^3} - 1} \right) \cdot \frac{d}<br />
{{dx}}{{\left( {4{x^2} + 1} \right)}^8} - {{\left( {4{x^2} + 1} \right)}^8} \cdot \frac{d}<br />
{{dx}}\left( {12{x^3} - 1} \right)}}<br />
{{{{\left( {12{x^3} - 1} \right)}^2}}} =  \ldots
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