Calculus

How do you find the derivative of (x-2)^.5 times (2x+1) times (x-3)^-.666666667? What is the final answer as well?

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  1. I see

    y = (2x+1)(x-2)^.5 / [(x-3)^(2/3)]

    There are many ways to do this to find dy/dx

    one is to use the quotient rule and just slug it out.

    If you know logs, there is a nice way:

    using the rules of logs we get

    ln y = (1/2)ln(x-2) + ln(2x+1) - (2/3)ln(x-3)

    then (dy/dx) / y = 1/(2(x-2)) + 2/(2x+1) - 2/[3(x-3)]

    multiply both sides by y, replacing y with the orignal function on the right side, and you have dy/dx

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