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Rigorous definition of "Differential"


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#21 studiot

studiot

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Posted 11 January 2017 - 11:24 PM

Dear old Leibnitz.

 

His notation is so convenient and flexible.

The main difficulty was typng the text, but no longer with modern computers or handwriting.

Writing f'(x) can be done on a single line. That was a good reason to introduce it.

 

Thank you for referring to Thomas & Finney (I have the 9th edition).

I think I have spotted your difficulty.

 

The differential defined on page 251 is dy, not dx

 

Using Leibnitz makes this more obvious 

 

 
y = f\left( x \right)
 
\frac{{dy}}{{dx}} = f'\left( x \right) differentiate with respect to x
 
dy = f'\left( x \right)dx
 
df\left( x \right) = f'\left( x \right)dx
 
 
but isn't dy clearer than the last line which is your original definition in post#1?
 
Note also that both dy and dx are classed as variables.

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