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Can someone go over my work for this derivative?

  1. Jul 23, 2011 #1
    1. The problem statement, all variables and given/known data

    Find dy/dx:

    [itex](3x^2+5x-2)^{sinx}[/itex]

    3. The attempt at a solution

    [itex]y = (3x^2+5x-2)^{sinx}[/itex]

    [itex]ln y = ln [(3x^2+5x-2)^{sinx}][/itex]

    [itex]ln y = sinx [ln(3x^2+5x-2)][/itex]

    [itex]\frac{1}{y} \frac{dy}{dx} = cosx[ln(3x^2+5x-2)] + sinx[\frac{6x+5}{3x^2+5x-2}][/itex]

    [itex]\frac{dy}{dx} = [3x^2+5x-2]^{sinx} [ cosx[ln(3x^2+5x-2)] + sinx[\frac{6x+5}{3x^2+5x-2}] ][/itex]
     
  2. jcsd
  3. Jul 23, 2011 #2
    That looks good to me.
     
  4. Jul 23, 2011 #3
    Last edited by a moderator: Apr 26, 2017
  5. Jul 23, 2011 #4
    Thanks fellas.
     
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