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Math Help - find derivative

  1. #1
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    find derivative

    x^3(square root of x + 1)

    x^3 * (x + 1)^(1/2)

    i'm stuck after this.
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  2. #2
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    Quote Originally Posted by algebra2 View Post
    x^3(square root of x + 1)

    y =x^3  (x + 1)^{\frac{1}{2}}

    i'm stuck after this.
    differentiate using product rule

    \frac{dy}{dx} = 3x^2 (x+1)^{\frac{1}{2}}+x^3\frac{1}{2}(x+1)^{\frac{-1}{2}}

    = 3x^2 (x+1)^{\frac{1}{2}}+\frac{x^3}{2\sqrt{x+1}}

    = \frac{6x^2 (x+1)+x^3}{2\sqrt{x+1}}

    = \frac{7x^3 +6x^2}{2\sqrt{x+1}}
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