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    Hi

    Can anyone help with this? I'm looking at an online example:

    Find the derivatives of the following functions:
    QUESTION
    ...(iii) y = 2?x.
    ANSWER
    ....(iii) when y = 2?x, this can be written as y = 2x(1/2).

    Therefore dy/dx = x-(1/2) = 1/(?x)


    I don't understand why y = 2?x can be written as y = 2x(1/2)! I've tried it using a number for x and you get double?
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    what is the ? supposed to represent?
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    2\sqrt{x} = 2x^{\frac{1}{2}}

    You mean this?
    You have to really make sure you write your questions out properly please lol...
    If you square root something, another way of writing it is "something" to the power of 1/2. That's simply it :P

    As for you getting the wrong answer when you pick a value for x... You are probably just not working it out/typing it into your calculator properly.
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    (Original post by mh1985)
    Hi

    Can anyone help with this? I'm looking at an online example:

    Find the derivatives of the following functions:
    QUESTION
    ...(iii) y = 2?x.
    ANSWER
    ....(iii) when y = 2?x, this can be written as y = 2x(1/2).

    Therefore dy/dx = x-(1/2) = 1/(?x)


    I don't understand why y = 2?x can be written as y = 2x(1/2)! I've tried it using a number for x and you get double?
    What do you mean?
    Does 'y=2?x' mean 'y=2^x'?
    And does 'y=2x(1/2)' mean 'y=2x^(1/2)'??
    I still can't help you out, but still, get your notation right.

    Edit: The guy above has made it clear
    • PS Helper
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    The laws of indices state that x^a \times x^b = x^{a+b}. Now, we know that \sqrt{x} \times \sqrt{x} = x, and since x=x^1, it makes sense that \sqrt{x} = x^{\frac{1}{2}}; then:
    \sqrt{x} \times \sqrt{x} = x^{\frac{1}{2}} \times x^{\frac{1}{2}} = x^{\frac{1}{2} + \frac{1}{2}} = x^1 = x

    Is your confusion coming from the 2? Because you should note that 2\sqrt{x} = 2x^\frac{1}{2} = 2 (x^\frac{1}{2}) \ne (2x)^{\frac{1}{2}} = \sqrt{2x}.
 
 
 
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