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Math Help - derivatives

  1. #1
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    derivatives

    Find y′ if

    y = (10x+3)^6x+7


    differentiate both sides with respect to x = ?


    solve for y' = ?
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  2. #2
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    Quote Originally Posted by pourcarlos View Post
    Find y′ if

    y = (10x+3)^6x+7


    differentiate both sides with respect to x = ?


    solve for y' = ?
    I assume that you mean:

    y = (10x+3)^{6x+7}

    If so re-write the term of the function to:

    y = e^{(6x+7) \cdot \ln(10x+3)}

    To differentiate this exponential function use chain rule and product rule:

    y'= e^{(6x+7) \cdot \ln(10x+3)} \cdot \left(\ln(10x+3) \cdot 6 + (6x+7) \cdot \dfrac1{10x+3} \cdot 10 \right)

    ... and now simplify.
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