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Differentiation

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..
Original post by ᒍack
How do I differentiate √x^3 / 2 ?


Write x3=x3/2\sqrt{x^3} = x^{3/2}. Proceed as normal.

The 2−1/22^{-1/2} is a coefficient of x so yes you keep it. The usual rule ddxaxn=anxn−1\dfrac{d}{dx} ax^n = anx^{n-1} applies
(edited 6 years ago)
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Original post by RDKGames
Write x3=x3/2\sqrt{x^3} = x^{3/2}. Proceed as normal.

The 2−1/22^{-1/2} is a coefficient of x so yes you keep it. The usual rule ddxaxn=anxn−1\dfrac{d}{dx} ax^n = anx^{n-1} applies


Ohhhhh, i misread ignore what was just wrote, thanks my dude!
(edited 6 years ago)
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Original post by RDKGames
Write x3=x3/2\sqrt{x^3} = x^{3/2}. Proceed as normal.

The 2−1/22^{-1/2} is a coefficient of x so yes you keep it. The usual rule ddxaxn=anxn−1\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!
(edited 6 years ago)
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:

ddx(2−1/2x3/2)=2−1/2ddx(x3/2)\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:

ddx(2−1/2x3/2)=2−1/2ddx(x3/2)\dfrac{d}{dx}(2^{-1/2}x^{3/2}) = 2^{-1/2} \dfrac{d}{dx}(x^{3/2})


I thought if  2−1/2\ 2^{-1/2} is the coefficient of  x3/2\ x^{3/2} then you would multiply  2−1/2by3/2\ 2^{-1/2} by 3/2 I feel like i'm missing it :/
(edited 6 years ago)
Original post by ᒍack
I thought if  2−1/2\ 2^{-1/2} is the coefficient of  x3/2\ x^{3/2} then you would multiply  2−1/2by3/2\ 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  3/2X1/2\ 3/2 X^{1/2} which was wrong
Original post by ᒍack
Ahh.. Ok, so I did go on to do this and ended up with the answer  3/2X1/2\ 3/2 X^{1/2} which was wrong


Seems to me like you forgot about the 2−1/22^{-1/2} at the front.
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Original post by RDKGames
Seems to me like you forgot about the 2−1/22^{-1/2} at the front.


I got this by doing  1/21/2∗3/2\ 1/2^{1/2} * 3/2 which gave me  3/41/2\ 3/4^{1/2} which gave me  3/2x1/2\ 3/2 x^{1/2}
(edited 6 years ago)
Original post by ᒍack
I got this by doing  1/21/2∗3/2\ 1/2^{1/2} * 3/2 which gave me  3/41/2\ 3/4^{1/2} which gave me  3/2x1/2\ 3/2 x^{1/2}


You essentially say that 21/2⋅2=41/22^{1/2 }\cdot 2 = 4^{1/2} which is not true.
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Original post by RDKGames
You essentially say that 21/2⋅2=41/22^{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 21/2⋅2=41/22^{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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