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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).

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.CR: Chapter 4 Review
Problem 4CR: Determine whether each of the following statements is true or false, and explain why. The derivative...
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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).
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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