Let h(x, y) be a differentiable function and let (xo, yo) be a point in the domain of h. Also, let u be a unit vector. Then D-u h(xo, yo) = -Du h(xo, yo).
Let h(x, y) be a differentiable function and let (xo, yo) be a point in the domain of h. Also, let u be a unit vector. Then D-u h(xo, yo) = -Du h(xo, yo).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let h(x, y) be a differentiable function and let (xo, yo) be a point in the domain of h. Also, let u be a
unit vector. Then
D- h(xo, yo) = -Du h(xo, yo).
Hint: Your job is to show that two directional derivatives are related. First notice the two negative signs.
One of them is the negative of a VECTOR. Start by computing the directional derivative on the LHS.
Remember that for the dot product, a (-b) = (-a) b=-(ab).
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