Let f(u) = u™ Au, where u e Rd and A e Rd×d is a symmetric matrix. Calculate Vuf(u).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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I need help on the last question of the three. 

• Let f(u) = aTu = E-1 a;U; for a, u E Rd. Calculate Vuf (u).
• Let f(u) = ||u||3 = E÷1 u? for u E Rd. Calculate Vuf(u).
• Let f(u) = uT Au, where u E Rd and A E Rdxd is a symmetric matrix. Calculate Vuf (u).
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Transcribed Image Text:• Let f(u) = aTu = E-1 a;U; for a, u E Rd. Calculate Vuf (u). • Let f(u) = ||u||3 = E÷1 u? for u E Rd. Calculate Vuf(u). • Let f(u) = uT Au, where u E Rd and A E Rdxd is a symmetric matrix. Calculate Vuf (u). и
Expert Solution
Step 1: Formula used and given.

Directional derivative: If the function f is differentiable at x, then the directional derivative exists along any vector v and it is given by,

vf(x)=f(x)·v

Given: f(u)=uTAu, ud and Ad×d is symmetric matrix.

To find: uf(u).

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