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Simple Differentials - please help?

  1. Oct 12, 2008 #1
    1. The problem
    Use Differentials to approximate (24.5)^(1/2) + (9.5)^(1/2). Compare your answer to your calculator's answer.

    2. Relevant equations

    I used z = (x)^(1/2) + (y)^(1/2)

    3. The attempt at a solution

    What I used:
    let z = (x)^(1/2) + (y)^(1/2)
    x = 25
    y = 10
    dx = 0.5
    dy = 0.5
    Using [​IMG].
    I plugged in 1/(2(x)^(1/2)) for the partial derivative w/respect to x, and 1/(2(y)^(1/2)) for the partial derivative w/respect to y. When I plug into the formula, I get 0.1290 not 8.0139 like in the calculator. What am I doing wrong?
    Last edited: Oct 12, 2008
  2. jcsd
  3. Oct 12, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    You the did the derivative wrong. The derivative of xn is n xn-1, not n xn as you have.
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