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Chain Rule: Derivatives

  1. Oct 1, 2008 #1
    Chain Rule

    Question is
    Find the derivative of F(x)= 3 sq rt of x^3-1

    First step I did was changing the Sq RT to (x^3-1)^3/2
    Then I solved it by 3/2(X^3-1)^1/2*3X^2

    Another problem very similar
    F(X)= 3 SQ RT of X^4+3x+2

    Step 1 (X^4+3x+2)^3/2
    Then 3/2(X^4+3x+2)*4x^3+3

    I know how to do the derivatives my only concern is that 3 in front of the square roots are throwing me off, I just want to know if I'm doing it right.
  2. jcsd
  3. Oct 1, 2008 #2
    so, your F(x) = 3*sqrt(x^3-1) ?

    if so, F'(x) = 3*[1/2(x^3-1)^-1/2]*3x^2 = (9x^2)/(2sqrt(x^3-1))
    Last edited: Oct 1, 2008
  4. Oct 1, 2008 #3
    It looks like you're trying to put the coefficient out front into the exponent, like saying 3*(x^1/2) = x^3/2, which it is not. With derivatives that coefficient just kinda stays put...
  5. Oct 1, 2008 #4
    [tex] 3\sqrt{x^3-1} = 3(x^3-1)^{1/2}[/tex]
    [tex]\frac{d}{dx}[3(x^3-1)^{1/2}] = \frac{1}{2} 3 (x^3-1)^{-1/2} 3x^2 = \frac{9x^2}{2\sqrt{x^3-1}}[/tex]

    just like jth01 said: [tex] 3x^{1/2} [/tex] does NOT equal [tex] x^{3/2} [/tex]
  6. Oct 1, 2008 #5
    Thanks guys.
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