Hyperbolic Functions with Constants k and m: dy/dx Formula

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SUMMARY

The discussion centers on the differentiation of the hyperbolic function defined as y=km(ln(cosh(gt/km)^(1/2))). The derivative dy/dx is expressed as gtanh((gt/km)^(1/2))/(2(gt/km)^(1/2)). Participants clarify the correct formulation of the function, debating between two interpretations: a) y = km ln(√(cosh(gt/(km))) and b) y = km ln(cosh(√(gt/(km)))). The consensus leans towards option b, indicating a need for precision in derivative notation, specifically dy/dt.

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y=km(ln(cosh(gt/km)^(1/2)))
constants k and m
dy/dx=gtanh((gt/km)^(1/2))/(2(gt/km)^(1/2))...?
 
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Don't think so, but I'm not sure how the problem is actually stated.

Is it
a)[tex]y = km~ln(\sqrt{cosh(gt/(km))}~)[/tex]

or
b)[tex]y = km~ln(cosh(\sqrt{gt/(km)}~))[/tex]
?
As you wrote the problem, it would be a, but your derivative (which should be dy/dt) suggests it is b.
 
b sorry my mistake I am working on the second derivative now it seems a bit to messy but I don't see an error in y'
 

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