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    How do I differentiate √x^3 / 2 ?

    I suppose what i'm actually trying to figure out is whether i can keep 2^1/2 on the bottom as a fraction when i differentiate..
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    (Original post by ᒍack)
    How do I differentiate √x^3 / 2 ?
    Write \sqrt{x^3} = x^{3/2}. Proceed as normal.

    The 2^{-1/2} is a coefficient of x so yes you keep it. The usual rule \dfrac{d}{dx} ax^n = anx^{n-1} applies
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    (Original post by RDKGames)
    Write \sqrt{x^3} = x^{3/2}. Proceed as normal.

    The 2^{-1/2} is a coefficient of x so yes you keep it. The usual rule \dfrac{d}{dx} ax^n = anx^{n-1} applies
    Ohhhhh, i misread ignore what was just wrote, thanks my dude!
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    (Original post by RDKGames)
    Write \sqrt{x^3} = x^{3/2}. Proceed as normal.

    The 2^{-1/2} is a coefficient of x so yes you keep it. The usual rule \dfrac{d}{dx} ax^n = anx^{n-1} applies
    How do you differentiate it when it was in the form: X^{3/2} ?
    I read the formula but have never seen it like that before, Cheers!
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    (Original post by ᒍack)
    How do you differentiate it when it was in the form: X^{3/2} ?
    I read the formula but have never seen it like that before, Cheers!
    The power of 2 is just a constant therefore it can be taken outside during the process of differentiation like so:

    \dfrac{d}{dx}(2^{-1/2}x^{3/2}) = 2^{-1/2} \dfrac{d}{dx}(x^{3/2})
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    (Original post by RDKGames)
    The power of 2 is just a constant therefore it can be taken outside during the process of differentiation like so:

    \dfrac{d}{dx}(2^{-1/2}x^{3/2}) = 2^{-1/2} \dfrac{d}{dx}(x^{3/2})
    I thought if \ 2^{-1/2} is the coefficient of \ x^{3/2} then you would multiply \ 2^{-1/2} by 3/2 I feel like i'm missing it :/
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    (Original post by ᒍack)
    I thought if \ 2^{-1/2} is the coefficient of \ x^{3/2} then you would multiply \ 2^{-1/2} by 3/2 I feel like i'm missing it :/
    You do. I haven't said anywhere that this isn't what you're doing.
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    (Original post by RDKGames)
    You do. I haven't said anywhere that this isn't what you're doing.
    Ahh.. Ok, so I did go on to do this and ended up with the answer \ 3/2 X^{1/2} which was wrong
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    (Original post by ᒍack)
    Ahh.. Ok, so I did go on to do this and ended up with the answer \ 3/2 X^{1/2} which was wrong
    Seems to me like you forgot about the 2^{-1/2} at the front.
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    (Original post by RDKGames)
    Seems to me like you forgot about the 2^{-1/2} at the front.
    I got this by doing \ 1/2^{1/2} * 3/2 which gave me \ 3/4^{1/2} which gave me \ 3/2   x^{1/2}
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    (Original post by ᒍack)
    I got this by doing \ 1/2^{1/2} * 3/2 which gave me \ 3/4^{1/2} which gave me \ 3/2   x^{1/2}
    You essentially say that 2^{1/2 }\cdot 2 = 4^{1/2} which is not true.
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    (Original post by RDKGames)
    You essentially say that 2^{1/2 }\cdot 2 = 4^{1/2} which is not true.
    Oops missed that thanks. Can you show me how you'd differentiate it please?
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    (Original post by RDKGames)
    You essentially say that 2^{1/2 }\cdot 2 = 4^{1/2} which is not true.
    ah... I found out the reason I wasn't getting it was because my book doesn't talk about the constant multiple rule.. now what you said makes sense to me :P
 
 
 
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