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Paul's Online Notes
Paul's Online Notes
Home / Calculus III / Partial Derivatives / Directional Derivatives
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Section 13.7 : Directional Derivatives

For problems 1 & 2 determine the gradient of the given function.

  1. f(x,y)=x2sec(3x)x2y3 Solution
  2. f(x,y,z)=xcos(xy)+z2y47xz Solution

For problems 3 & 4 determine Duf for the given function in the indicated direction.

  1. f(x,y)=cos(xy) in the direction of v=3,4 Solution
  2. f(x,y,z)=x2y34xz in the direction of v=1,2,0 Solution
  3. Determine Duf(3,1,0) for f(x,y,z)=4xy2e3xz in the direction of v=1,4,2. Solution

For problems 6 & 7 find the maximum rate of change of the function at the indicated point and the direction in which this maximum rate of change occurs.

  1. f(x,y)=x2+y4 at (2,3) Solution
  2. f(x,y,z)=e2xcos(y2z) at (4,2,0) Solution