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Math Help - Find the derivative of the following equation in fully simplified form

  1. #1
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    Find the derivative of the following equation in fully simplified form

    G(x)=3x * (1-2x^2)^-1/3
    I have attached my attempt at the question but I'm sure it's not right.Find the derivative of the following equation in fully simplified form-image.jpg
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  2. #2
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    Re: Find the derivative of the following equation in fully simplified form

    It's pretty close to being right! Your function is G(x)= 3x(1- 2x^2)^{-1/3} and, using the product rule and chain rule, you have
    G'(x)= 3x(-1/3)(1- 2x^2)^{-4/3}(-4x)+ (1- 2x^2)^{-1/3)(3), which is correct.

    But you appear to be canceling that "-1/3" with the "3" at the end of the formula. You cannot do that because they are not multiplied together. You can cancel the "1/3" with the "3" at the beginning of the fomula: G'(x)= 4x^2(1- 2x^2)^{-4/3}+ 3(1- 2x^2)^{-1/3}. You can, in addition, factor (1- 2x^2)^{-1/3} out: (1- 2x^2)^{-1/3}(4x^2(1- 2x^2)^{-1}+ 3).
    Last edited by HallsofIvy; April 10th 2013 at 01:49 PM.
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  3. #3
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    Re: Find the derivative of the following equation in fully simplified form

    You have a lot of algebraic mistakes.

    In line 2, why did you cross out the 1/3 and 3 (on the right)? They do not cancel out because they are not being multiplied together, notice there is a plus in between them. The 1/3 and the 3 (on the left) can cancel out because they're being multiplied.

    In the third line, why did you randomly cross out (1-2x^2)^{-1/3}

    In the forth line, you cannot bring the (1-2x^2)^{1/4} like that. Can you see your mistake?
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    Re: Find the derivative of the following equation in fully simplified form

    Thank you all for your replies. I have used your advice and I have attached my final answer
    Attached Thumbnails Attached Thumbnails Find the derivative of the following equation in fully simplified form-image.jpg  
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  5. #5
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    Re: Find the derivative of the following equation in fully simplified form

    Hello, digidako!

    \text{Differentiate and simplify: }\:G(x)\:=\:\frac{3x}{(1-2x^2)^{\frac{1}{3}}}

    G'(x) \;=\;\frac{(1-2x^2)^{\frac{1}{3}}\cdot 3 \:-\:3x\cdot\frac{1}{3}(1-2x^2)^{-\frac{2}{3}}\cdot(-4x)}{(1-2x^2)^{\frac{2}{3}}}

    . . . . . =\;\frac{3(1-2x^2)^{\frac{1}{3}} + 4x^2(1-2x^2)^{-\frac{2}{3}}}{(1-2x^2)^{\frac{2}{3}}}

    . . . . . =\;\frac{(1-2x^2)^{-\frac{2}{3}}\cdot\left[3(1-2x^2) + 4x^2\right]}{(1-2x^2)^{\frac{2}{3}}}

    . . . . . =\;\frac{3-6x^2+4x^2}{(1-2x^2)^{\frac{4}{3}}}

    G'(x) \;=\;\frac{3-2x^2}{(1-2x^2)^{\frac{4}{3}}}
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