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
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Chapter2: Second-order Linear Odes
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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
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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