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calculus

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find the derivative of the function (6x+1)/(19x+1)^1/2

PLEASE EXPLAIN IM LOST

  • calculus - ,

    You use the quotient rule of :[u'v -uv']/v^2
    so:

    u=(6x+1) v=(19x+1)^1/2
    u'=6 v'= [1/2(19x+1)^-1/2] (19)

    y' = 6[(19x+1)^1/2] - (6x+1)[1/2(19x+1)^-1/2] (19)
    you can simplify it by taking a common factor. In this case its easier to take (19x+1)^-1/2--- Always take the lowest common factor.

    y'=[[19x+1]^-1/2] 6(19x+1) -(6x+1)(1/2)(19)
    y'=[[19x+1]^-1/2] 114x+6-57x+9.5
    Final answer:
    y'=[[19x+1]^-1/2] 57x + 15.5

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