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Derivative Problem

  1. Jun 12, 2004 #1
    My algebra continues to let me down…

    How about this one…I know there a simpler ways to do these problems but at this point I’m supposed to do it the hard way.

    Using the definition of derivate find f ` (x)

    f(x) = SQRT(1-3x)

    f ` (x) = lim h->0 [(f(x+h)) – (f(x))]/h

    = lim->0 [(SQRT(1-3(x+h))) – (SQRT(1-3x))]/h

    = lim->0 [[(SQRT(1-3(x+h))) – (SQRT(1-3x))]/h] . [[((SQRT(1-3x-3h))) + (SQRT (1-3x))]/ [((SQRT(1-3x-3h))) + (SQRT (1-3x))]]

    =lim->0 (1-3x-3h-1+3x)/(h[(SQRT(1-3x-3h)) + (SQRT (1-3x))]

    = lim->0 -3/[SQRT(1-3x-3h) + SQRT (1-3x)]

    = -3/(2(SQRT(1-3x))
     
  2. jcsd
  3. Jun 12, 2004 #2

    arildno

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    Dearly Missed

    Why are you let down by the correct answer? :smile:
     
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