Show that StartFraction d Over dx EndFraction(ln kx)equalsStartFraction d Over dx EndFraction ln x, given that xgreater than 0 and kgreater than 0 is a real number.
Show that StartFraction d Over dx EndFraction(ln kx)equalsStartFraction d Over dx EndFraction ln x, given that xgreater than 0 and kgreater than 0 is a real number.
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter2: Basic Linear Algebra
Section: Chapter Questions
Problem 15RP
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Question
Show that StartFraction d Over dx EndFraction
(ln kx)equalsStartFraction d Over dx EndFraction ln x,
given that xgreater than
0
and kgreater than
0
is a real number.
Expert Solution
Step 1
Answer:
To show that StartFraction d Over dx EndFraction(ln kx) equals StartFraction d Over dx EndFraction(ln x), we can simply use the chain rule of differentiation.
Let y = ln kx, then we can rewrite it as:
y = ln k + ln x
Taking the derivative of both sides with respect to x:
StartFraction d y Over dx EndFraction = StartFraction d Over dx EndFraction (ln k + ln x)
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