Prove the differentiation formula. dx Let y = sech (x), then, in exponential terms, y = 11 [sech(x)] = -sech(x) tanh(x) Taking the derivative, in exponential terms, gives the following. dy dx 11 -2 = -sech(x) tanh(x) + e-x ex + e-x X
Prove the differentiation formula. dx Let y = sech (x), then, in exponential terms, y = 11 [sech(x)] = -sech(x) tanh(x) Taking the derivative, in exponential terms, gives the following. dy dx 11 -2 = -sech(x) tanh(x) + e-x ex + e-x X
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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![Prove the differentiation formula.
d
dx
Let y = sech(x), then, in exponential terms, y =
dy
dx
-[sech(x)]-sech(x) tanh(x)
Taking the derivative, in exponential terms, gives the following.
=
-2
= -sech(x) tanh(x)
e-x
ex + e-x
e-x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7b56d21-7f05-4c85-8732-b566027c761e%2F4df67ad2-b779-4012-a4f2-625df297a5e8%2Fw539xwg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Prove the differentiation formula.
d
dx
Let y = sech(x), then, in exponential terms, y =
dy
dx
-[sech(x)]-sech(x) tanh(x)
Taking the derivative, in exponential terms, gives the following.
=
-2
= -sech(x) tanh(x)
e-x
ex + e-x
e-x
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