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-   -   Finding the derivative of 1/square root of X with definition (https://www.askmehelpdesk.com/showthread.php?t=460171)

  • Mar 24, 2010, 05:51 PM
    smc123
    Finding the derivative of 1/square root of X with definition
    Can any one help me with finding the derivative of 1/x^(1/2) or square root of X using the definition F(x+h)-F(x)/h

    I tried conjugating, using negative exponents but I only get really close.

    Using the power rule F'(x) is clearly -1/2x^(3/2) but using the definition is more difficult
  • Mar 25, 2010, 09:18 AM
    ebaines

    Try this (for ease of typing I'm leaving the limit symbol):

    Multiply through by :



    Whenever you have the difference of square roots like this it helps to multiply the numerator and denominator by the sum of those roots, and see where it takes you:



    Now take the limit as h goes to 0.

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