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Calc

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Find f'(7) for f(x)=6x^ln(x)

  • Calc -

    Use chain rule.
    Let
    y=6xln(x)
    take log on both sides:
    ln(y) = ln(6)+ln(x)*ln(x)
    ln(y) = ln(6) + ln²(x)
    differentiate both sides w.r.t. x
    (1/y)y' = 0 + 2ln(x)*(1/x)
    y' = dy/dx
    = y*2ln(x)*(1/x)
    = 6xln(x)*2ln(x)*(1/x)
    = 12xln(x)-1*ln(x)

    Check my calculations.

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