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Math Help - differentiate question

  1. #1
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    differentiate question

     <br />
y=\sqrt{x^3} (x+1)<br />

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

     <br />
\frac{1}{3}x^\frac{-1}{2}<br />

    im unsure about this can anyone help or correct me? many thanks
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  2. #2
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    y=x^{\frac{2}{3} +1} + x^{\frac{2}{3}}

    then

    y'=\left(\frac{2}{3} +1 \right)\cdot x^{\frac{2}{3} +1 -1} + \left(\frac{2}{3}\right)\cdot x^{\frac{2}{3}-1}
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  3. #3
    NRS
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    Youre going to have to use the chain rule

    First of all, is not correct, x cubed will be to the one half power, because you are taking the square root of it, not the cube root.

    To differentiate, you multiply ((x^3)^(1/2)) and x^(1) to get

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

    Now, differentiate:

    dy/dx = (3/2)(x^3)^(1/2)*(3x^2)
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  4. #4
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    You also appear not to have "distributed":

    y= \sqrt{x^3}(x+1)= x^{3/2}(x+1)= x^{5/2}+ x^{3/2}

    Now, use that the derivative of x^n is nx^{n-1}.
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