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Estimating partial derivatives/directional derivatives

  1. Nov 10, 2008 #1
    1. The problem statement, all variables and given/known data
    Let z = f(x,y) be a differentiable function on R^2 such that f(1, 2) = 3,
    f(1.2, 2.3) = 3.4 and f(0.9, 2.1) = 3.2.

    a) Estimate dz/dx and dz/dy at (1,2) (dz/dx and dz/dy are partial derivatives)
    b) Estimate the value of the directional derivative of z = f(x,y) at the point (1,2) as you move towards (2,3)

    2. Relevant equations

    3. The attempt at a solution
    I've tried using the formal definitions of directional and partial derivatives to do these but I just can't get how the estimates come in. Help would be very much appreciated
  2. jcsd
  3. Nov 10, 2008 #2


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    Science Advisor
    Homework Helper

    A finite difference quotient estimates the derivative, since the derivative is the limit of the difference quotient as the difference goes to zero. The given values will let you estimate the directional derivative in the direction parallel to (0.2,0.3) and (-0.1,0.1). Use those to estimate the directional derivatives in the directions (1,0) and (0,1). Which are the two partial derivatives.
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