5.6 Differentiate f with respect to t and g with respect to X, where
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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![**5.6** Differentiate \( f \) with respect to \( t \) and \( g \) with respect to \( X \), where
\[
f(t) = \sin(\log(t^\top t)), \quad t \in \mathbb{R}^D
\]
\[
g(X) = \text{tr}(AXB), \quad A \in \mathbb{R}^{D \times E}, \, X \in \mathbb{R}^{E \times F}, \, B \in \mathbb{R}^{F \times D},
\]
where \(\text{tr}(\cdot)\) denotes the trace.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd4ed983c-8942-4ca0-93d1-8e13c157c75d%2Feee41355-3e16-41e0-a036-a2bf6b133118%2Fcqwn02_processed.png&w=3840&q=75)
Transcribed Image Text:**5.6** Differentiate \( f \) with respect to \( t \) and \( g \) with respect to \( X \), where
\[
f(t) = \sin(\log(t^\top t)), \quad t \in \mathbb{R}^D
\]
\[
g(X) = \text{tr}(AXB), \quad A \in \mathbb{R}^{D \times E}, \, X \in \mathbb{R}^{E \times F}, \, B \in \mathbb{R}^{F \times D},
\]
where \(\text{tr}(\cdot)\) denotes the trace.
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