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    Hi,
    can you help me how to differentiate roots?

    Look at this one:

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    thank you in advance <3

    €: I know how to do the dy/dx part, but I don't understand how they've changed the root into the fractional form :?
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      You should remember that anything to the power of a half means you square root it. So 4^{1/2} = 2, for example. Also remember that anything to the power of -1 is "one over" that number. So 4^{-1} = \frac{1}{4}.

      Then you can put the two rules together if needed. For example, 4^{-1/2} = \frac{1}{4^{1/2}} = \frac{1}{2}

      Is that now clear?
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      well with your example:

      y = 1/4x^-1/2

      dy/dx = (1/4 * -1/2) * x ^ (-1/2 -1)

      Bring the power down and multiply it

      After bring down the power, we need to minus it by 1


      dy/dx = -1/8x^-3/2
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      (Original post by StylaBoy)
      Hi,
      can you help me how to differentiate roots?

      Look at this one:

      Spoiler:
      Show


      thank you in advance <3

      €: I know how to do the dy/dx part, but I don't understand how they've changed the root into the fractional form :?
      You should know the following base identities
      \displaystyle x^{\frac{p}{q}}=\sqrt[q]{x^p}=\left( \sqrt[q]{x}\right) ^p
      where x>0 and
      x^{-k}=\frac{1}{x^k}
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      1 over 4x^{\frac12} can be turned into 1/4 of x to the negative 1/2 because that fraction can be split up into two parts: one over the square root of x multiplied by one over 4. By now you should know that the square root of x equals x to the power 1/2, and one over the square root of anything equals that to the negative 1/2). This is very basic stuff.
     
     
     
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