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Differentiating Square Roots

  1. Oct 27, 2010 #1
    Hi so I am new to calculus and need help with differentiation

    The question is:
    Differentiate the following function:

    sqrt(x^2-8x+20)

    So far I have gotten
    =(x^2-8x+20)^(1/2)
    =(1/2)(x^2-8x+20)^(-1/2) * 2x-8

    I am unsure where to go from here
    I know we are supposed to use the chain rule but I am still confused where to go after this step.

    Thanks
     
  2. jcsd
  3. Oct 27, 2010 #2

    Mark44

    Staff: Mentor

    You have
    sqrt(x^2-8x+20)
    =(x^2-8x+20)^(1/2)
    Up to here, what you have done is rewrite the expression in a different form.

    What you have below is the derivative of the expression above. It is not equal to what you started with, so you should not have =. This is the derivative, and it is mostly correct (you need parentheses around 2x-8.

    =(1/2)(x^2-8x+20)^(-1/2) * 2x-8

    Be sure to distinguish between the function you're differentiating and what you get when you differentiate (the deriviative). Here's one way:

    y = sqrt(x^2-8x+20) = (x^2-8x+20)^(1/2)

    dy/dx = (1/2)(x^2-8x+20)^(-1/2) * (2x-8)
    = (1/2)(2x - 8)/(x^2 - 8x + 20)^(1/2) = (x - 4)/(x^2 - 8x + 20)^(1/2)

    You can also write dy/dx as y'.
     
  4. Nov 2, 2010 #3
    Thank-you!
     
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